UC-NRLF 


B    3    112    M37 

PRINCIPLES  OF  COMBUSTION 

IN 

THE  STEAM  BOILER 
FURNACE 


•By 
ARTHUR  D.  PRATT 


Published  fy 

THE  BABCOCK  &  WILCOX  CO, 
NEW  YORK 


GIFT  OF 


D  SPT^ 


PRINCIPLES  OF  COMBUSTION 

IN 

THE  STEAM  BOILER 
FURNACE 


By 

ARTHUR  D.  PRATT 

\\ 


Published  by 

THE  BABCOCK  &  WILCOX  CO. 
NEW  YORK 


Engineering 
Library 


Copyright,  1920,  by 

The  Babcock  &  Wilcox  Co. 

Third  Issue 


Bartlett  Orr  Press 
New  York 


PRINCIPLES  OF  COMBUSTION  IN 

THE  STEAM  BOILER 

FURNACE 


I     INTRODUCTION 7 

II     THE  CHEMISTRY  OF  COMBUSTION         ....  9 

III  DENSITY,  WEIGHT  AND  VOLUME  OF  GASES      .       .  15 

IV  HEAT  OF  COMBUSTION 20 

V     SPECIFIC  HEAT 22 

VI     TEMPERATURES  DEVELOPED  IN  COMBUSTION    .       .  35 

VII     Am  AND  COMBUSTION 42 

VIII     COMBUSTION  FORMULAE 49 

IX     COMBUSTION  LOSSES 60 

X     SMOKE 67 

XI     GENERAL  CONCLUSIONS 70 

XII     THE  COMPUTATION  OF  COMBUSTION  DATA       .       .  72 

COAL 72 

WOOD 78 

OIL  .       .       .       .     ' 83 

NATURAL  GAS 87 

BY-PRODUCT  COKE  OVEN  GAS 95 

BLAST  FURNACE  GAS 100 

XIII     HEAT  BALANCE 105 

SOLID  OR  LIQUID  FUELS    .       .       .       .       .       .105 

GASEOUS  FUELS 108 


INTRODUCTION 

THE  function  of  a  boiler  furnace  is  the  generation  of  the 
maximum  amount  of  heat  from  a  given  quantity  of  a 
specific  fuel,  and  if  such  function  is  to  be  properly  fulfilled, 
it  is  essential  that  the  furnace  operator  understand  the  broader 
principles  involved  in  combustion.  Unfortunately,  from  the 
standpoint  of  efficient  steam  generation,  the  statement  is  too 
frequently  accepted  as  true  that  theoretical  generalizations  and 
mathematical  formulae  are  of  but  little  value  to  the  operating 
engineer.  To  an  extent,  such  statements  may  be  true,  but  on 
the  other  hand  it  is  to  be  remembered  that  combustion  is  purely 
a  chemical  phenomenon  and  as  such  can  be  properly  investigated 
and  controlled  only  by  chemical  means.  Experience  resulting 
from  the  "cut  and  try"  methods  of  ordinary  actual  practise  in 
the  burning  of  individual  fuels  is  unquestionably  an  important 
factor  in  the  bringing  about  of  efficient  furnace  results,  but  it  is 
obvious  that  such  results  will  be  most  readily  secured  when  this 
experience  is  combined  with  a  full  knowledge  of  the  theory  of 
combustion  and  the  proper  application  of  the  available  methods 
used  in  obtaining  combustion  data.  Further,  the  importance  of 
such  knowledge  is  today  greater  than  it  has  ever  been.  Most 
apparatus  for  the  generation  of  power  has  reached  a  state  of 
development  where  there  is  but  little  likelihood  of  any  great  in- 
crease in  economy.  The  generally  accepted  types  of  steam  boiler 
used  in  present  day  power  plant  practise  have  the  inherent  ability 
to  absorb  heat  efficiently  and  from  this  standpoint  may  be  included 
with  the  apparatus  from  which  much  more  cannot  be  expected. 
If  we  accept  this  statement  as  true,  the  efficient  generation 
of  steam  in  the  boiler  proper  becomes  in  reality  a  question  of 
efficient  combustion,  and  it  is  this  phase  of  boiler  practise — 
the  efficient  generation  of  heat  in  the  boiler  furnace — in  which 
there  is  the  greatest  and  in  fact  the  only  field  for  appreciable 
improvement. 

Power  plant  owners  are  coming  more  and  more  to  appreciate 
the  necessity  for  intelligence  in  the  boiler  room — the  reinforcing 
of  experience  in  firing  by  a  full  knowledge  of  the  theory  of  com- 
bustion— and  in  the  growing  number  of  plants  where  this  need 
is  realized  suitable  apparatus  is  installed  for  the  determination 


and  checking  of  combustion  results.  In  plants  not  so  equipped, 
the  possible  savings  due  to  the  intelligent  use  of  such  apparatus 
and  the  proper  application  of  the  data  so  obtained  in  reducing 
preventable  losses,  are  in  the  aggregate  enormous. 


THE  CHEMISTRY  OF  COMBUSTION 

THE  chemistry  of  combustion  as  applied  to  boiler  furnace 
practise  is  elementary,  but  for  a  proper  comprehension  of 
the  subject  it  seems  advisable  to  include  a  brief  con- 
sideration of  the  general  principles  involved,  together  with  data 
covering  the  combining  qualities  of  the  constituents  of  the  fuels 
ordinarily  encountered  in  steam  generation. 

The  smallest  quantity  of  an  element  or  a  compound  that 
is  capable  of  separate  existence  is  taken  as  the  physical  unit 
of  matter  and  is  called  a  molecule.  Molecules  are  composed  of 
atoms  of  elements  which  may  be  denned  as  the  smallest  unit 
of  an  element  which  can  enter  into  or  be  expelled  from  a  com- 
pound. Atoms  never  exist  singly  but  in  combination  with  one 
or  more  atoms  to  form  a  molecule.  Molecules  of  the  elementary 
gases,  such  as  oxygen,  nitrogen  and  hydrogen,  are  supposed  to 
consist  of  two  atoms. 

A  chemical  reaction  between  elements  or  compounds  is  a 
rearrangement  of  the  atoms  of  the  constituent  elements  into 
a  new  combination  of  molecules.  Such  reactions  always  occur 
in  accordance  with  fixed  and  invariable  weight  relations  which  are 
characteristic  of  the  elements  involved,  and  definite  volumetric 
changes  based  on  the  number  of  gaseous  molecules  reacting  and 
produced. 

Elements  are  designated  by  symbols,  and  compounds  by 
combinations  of  the  symbols  of  their  constituent  elements. 
Subscripts  are  affixed  to  the  symbols  to  designate  the  number 
of  times  the  combining  or  atomic  weight  of  the  element  occurs. 
It  follows  that  from  the  symbol  of  a  compound  so  expressed  and 
the  atomic  weight  of  the  elements  involved,  the  proportionate 
parts  by  weight  of  the  various  constituents  entering  into  the  com- 
pound may  be  readily  determined. 

The  elementary  substances  encountered  in  combustion  work 
are  oxygen,  nitrogen,  hydrogen,  carbon  and  sulphur.  The 
symbols  of  these  elements  together  with  their  atomic  weights 
are  given  in  Table  i,  page  10. 

COMBUSTION 

Combustion  is  the  phenomenon  resulting  from  any  chemical 
combination  evolving  heat.  Oxygen  is  the  sole  supporter  of 


I     >    - 


combustion,  and  a  combustible  therefore  may  be  defined  as  a 
substance  capable  of  combining  with  oxygen  to  produce  heat. 
The  speed  of  combustion  depends  upon  the  affinity  of  the  com- 
bustible element  for  oxygen,  and  to  a  lesser  extent  upon  the 
conditions  under  which  combustion  takes  place.  This  speed 
may  vary  from  the  very  slow,  as  in  the  case  of  rust  formation,  to 
the  instantaneous,  as  in  the  explosion  of  confined  powder. 

From  the  standpoint  of  heat  production  for  steam  generating 
purposes,  combustion  may  be  defined  as  the  rapid  combination 
of  the  combustible  elements  of  fuel  with  oxygen,  while  in  this 
sense  the  term  combustible  implies  the  capacity  of  an  element 
for  combining  rapidly  with  oxygen  to  produce  heat. 

Combustion  is  said  to  be  complete  when  the  combustible 
elements  and  compounds  have  united  with  all  of  the  oxygen  with 
which  they  are  capable  of  entering  into  combination. 

TABLE  1 
ELEMENTS  AND  COMPOUNDS    ENCOUNTERED  IN  COMBUSTION 


Substance 

Molecular 
Symbol 

Atomic  Weight 

Molecular  Weight 

Form 

Accurate 

Approxi- 
mate 

Accurate 

Approxi- 
mate 

Carbon 

c* 

H2 
02 
S2 
N2 
CO 
C02 
CH4 
C2H2 
C2H4 
C2H6 
S02 
H2S 
H20 

12.005 
1.008 
1  6.00 
32.07 
14.01 

12 

I 

16 
32 
14 

t 
2.015 
32.00 
6414 
28.02 
28.01 
44.01 
16.03 
26.03 
28.03 

30-OS 
64.07 
34.08 

18.02 

28.94 

2 
32 
64 
28 
28 

44 
16 
26 
28 
30 
64 
34 
18 

29 

Solid 
Gas 
Gas 
Solid 
Gas 
Gas 
Gas 
Gas 
Gas 
Gas 
Gas 
Gas 
Gas 
Vapor 
Gas 

Hydrogen     .... 
Oxygen                       • 

Sulphur    
Nitrogen  J     .... 
Carbon  Monoxide     . 
Carbon  Dioxide    .    .   • 
Methane                     »   ^ 

Acetylene     .     .     .     , 
Ethylene       .     . 
Ethane     .     .     .     .     . 
Sulphur  Dioxide   .     . 
Hydrogen  Sulphide  . 
Water  Vapor    .     .     . 
Air                     .    .     . 

::: 

*  ,  *    * 

*Atomic  symbol. 

tThe  molecular  weight  of  C  has  not  been  definitely  determined.  Carbon  exists  in  a 
number  of  forms  each  of  which  probably  has  its  own  molecular  weight.  The  latest  investi- 
gations indicate  that  a  molecule  of  carbon  in  any  form  consists  of  at  least  12  atoms. 

$  Atmospheric  nitrogen  as  distinguished  from  chemically  pure  nitrogen  which  has  an 
atomic  weight  slightly  less  than  14.01. 


10 


For  the  commercial  production  of  heat  it  is  essential  that 
the  combustible  elements  have  a  strong  and  ready  affinity  for 
oxygen.  Carbon  and  hydrogen  which  are  by  far  the  most  im- 
portant of  combustible  elements  encountered  in  the  common 
fuels  meet  this  requirement  admirably.  These  occur  either  in 
a  free  or  combined  state  in  all  fuels,  liquid,  solid  and  gaseous. 

The  combustible  elements  and  the  compounds  in  which  they 
appear  in  any  of  the  fuels  used  for  commercial  heat  generation 
are  given  in  Table  i.  This  table  gives  the  symbols  of  the 
elements  and  their  compounds  which  occur  in  combustion  work 
together  with  their  molecular  weights.  It  also  includes  the  non- 
combustible  elements  and  compounds,  a  knowledge  of  which  is 
necessary  in  the  obtaining  and  application  of  combustion  data. 

AIR 

As  we  find  in  nature  the  combustible  matter  for  the  generation 
of  heat,  so  from  the  same  source  we  obtain,  in  the  oxygen  of  the 
air,  the  necessary  supporter  of  combustion. 

Atmospheric  air  is  a  mechanical  mixture — as  distinguished 
from  a  chemical  compound — of  oxygen,  nitrogen,  and  slight 
amounts  of  carbon  dioxide,  water  vapor,  argon  and  other 
inert  gases.  For  engineering  purposes  the  carbon  monoxide 
and  the  inert  gases  are  ordinarily  included  with  the  nitrogen  and 
of  the  slightly  varying  proportions  of  oxygen  and  nitrogen  given 
by  different  authorities  the  generally  accepted  values  are  : 

By  Volume  By  Weight 

Per  Cent  Per  Cent 

O2  20.91  23.15 

N2  79.09  76.85 

The  oxygen  with  its  strong  affinity  for  the  combustible  con- 
stituents of  the  fuel,  under  the  proper  conditions  of  temperature 
which  will  be  discussed  hereafter,  separates  itself  from  its 
mechanical  union  with  nitrogen  and  enters  into  chemical  combi- 
nation with  the  available  combustible,  thus  fulfilling  its  function 
in  the  promotion  of  combustion.  The  nitrogen  serves  no  purpose 
in  combustion  and  in  fact  is  a  source  of  direct  loss  in  that  it 
absorbs  heat  in  its  passage  through  the  furnace  and  carries  off 
a  portion  of  such  heat  in  leaving  the  boiler ;  further,  as  a  useless 
constituent  it  necessitates  in  the  design  of  the  furnace,  boiler 

ii 


and  flue,  space  for  its  accommodation,  which,  were  it  possible 
or  practicable  to  supply  oxygen  alone  to  the  fuel,  would  not 
be  required. 

The  combination  of  oxygen  with  the  combustible  elements  and 
compounds  is,  as  stated,  in  accordance  with  fixed  laws.  Considered 
as  a  chemical  reaction  the  manner  of  such  combination  is  simple 
and  may  be  readily  computed  from  the  molecular  weights  given 
in  Table  i.  Assuming  complete  combustion  and  that  the  exact 
amount  of  oxygen  required  is  supplied  and  utilized  in  combination, 
these  reactions  and  the  resulting  combinations  are  as  given  in 
Table  2. 

TABLE  2 
CHEMICAL  REACTIONS  OF  COMBUSTION 


Combustible  Substance 

Reaction 

Carbon  (to  CO) 

2C+    02  =  2CO 

Carbon  (to  CO2) 

2C+2O2  =  2CO2 

Carbon  Monoxide 

2CO+  O2  =  2CO2 

Hydrogen 

2H2+  02  =  2H20 

Sulphur  (to  SO  2) 

S+  O2=SO2 

Sulphur  (to  SO8) 

2S+302  =  2S03 

Methane 

CH4+2O2=CO2  +2H2O 

Acetylene 

2C2H2+502=4C02+2H20 

Ethylene 

C2H4+302=2C02+2H20 

Ethane 

2C2H6+702=4C02+6H20 

Hydrogen  Sulphide 

2H2S+302  =  2H20-f2S02 

It  is  important  to  note  from  this  table  that  carbon  may  enter 
into  combination  with  oxygen  to  form  two  compounds,  carbon 
monoxide  and  carbon  dioxide.  In  burning  to  carbon  monoxide, 
carbon  has  not  combined  with  all  of  the  oxygen  with  which  it  is 
capable  of  entering  into  combination  and  is  not  therefore  com- 
pletely oxidized.  In  burning  to  carbon  dioxide  it  has  combined 
with  all  of  the  oxygen  possible  and  oxidization  is  complete.  Carbon 
monoxide  may  unite  with  an  additional  amount  of  oxygen  to  form 
carbon  dioxide  and  in  this  way  the  carbon  of  the  original  com- 
bination may  become  completely  oxidized.  The  fact  that  carbon 
may  enter  into  these  two  combinations  with  oxygen  is  of  the 
greatest  importance  in  furnace  efficiency  and  will  be  discussed 
hereafter  at  greater  length  in  the  consideration  of  the  heat  of 
combustion  and  air  supply. 


TEMPERATURE 

Before  discussing  in  detail  the  effects  of  supplying  oxygen 
for  combustion  in  excess  of  the  requisite  amount  or  of  supplying 
less  than  the  amount  required,  the  other  important  factor  of 
combustion,  viz.,  temperature,  should  be  considered. 

The  speed  of  combustion  is,  as  stated,  dependent  upon  the 
affinity  of  the  combustible  matter  for  oxygen  and  the  conditions 
under  which  combustion  takes  place.  The  chief  of  these  con- 
ditions is  that  of  temperature.  The  mere  fact  that  oxygen  is 
brought  into  the  presence  of  a  combustible  substance  does  not  of 
necessity  mean  that  combustion  will  follow. 

Every  combustible  substance  has  a  temperature  called  its 
ignition  temperature  to  which  it  must  be  brought  before  it  will 
unite  in  chemical  combination  with  oxygen  and  below  which  such 
combination  will  not  take  place;  and  this  ignition  temperature 
must  exist  with  oxygen  present  or  there  will  be  no  combustion. 

The  ignition  temperature  of  different  combustible  substances 
varies  greatly.  These  temperatures  for  various  fuels  and  for  the 
combustible  constituents  of  the  fuels  used  in  boiler  practise  are 
given  in  Table  3. 

TABLE  3 
IGNITION  TEMPERATURES 


Combustible  Substance 

Molecular 
Symbol 

Ignition  Temperature 
Degrees  Fahrenheit 

Sulphur  

So 

47° 

Fixed.  Carbon     Bituminous  Coal 

766 

Fixed  Carbon  —  Semi-bituminous  Coal  . 
Fixed  Carbon  —  Anthracite  Coal    .     .     . 

C.H, 

870 

925 
QOO 

Ethane                  .          

C,H« 

IOOO 

Ethylene 

C«H, 

IO22 

Hydrogen   

^axi4 
H, 

I  I^O 

Methane           . 

CH, 

I2O2 

Carbon  Monoxide 

CO 

I2IO 

It  is  of  interest  to  note  that  the  temperature  of  ignition  of 
the  gases  of  a  coal  vary  from  each  other  (see  flame)  and  are 
considerably  higher  than  the  ignition  temperature  of  the  fixed 
carbon  of  the  coal.  The  ignition  temperature  of  coal  is  the 
ignition  temperature  of  its  fixed  carbon  content,  since  the  gaseous 


constituents  are  ordinarily  distilled  off,  though  not  ignited,  before 
such  temperature  is  attained. 

When  combustion  has  started,  the  heat  evolved  in  the 
oxidization  of  the  combustible  matter  will  maintain  under  proper 
conditions  sufficiently  high  temperatures  for  further  ignition. 


DENSITY,  WEIGHT  AND  VOLUME  OF 

GASES 

IN  the  computation  of  combustion  data  it  is  frequently  neces- 
sary to  know  the  density,  weight  and  volume  of  air  and  of 
the  various  gases  encountered  in  commercial  practise. 
The  density  of  a  gas  (commonly  expressed  by  the  symbol  A) 
which  is  ordinarily  referred  to  that  of  air  as  standard,  is  the  weight 
of  unit  volume  of  the  gas  divided  by  the  weight  of  an  equal 
volume  of   pure   dry  air,   the   conditions  of   temperature   and 
pressure  being  the  same. 

The  weight  per  cubic  foot  of  a  gas,  ordinarily  designated  by 
S,  is,  under  standard  conditions,  called  the  specific  weight.  With 
the  weight  of  air  at  atmosphere  pressure  and  varying  temperature 
conditions  known,  the  weight  of  any  gas  at  the  same  temperature 
may  be  computed  from  the  relations  of  density  and  specific  weight 
as  indicated  by 

S,=S,  (air)  x  A  (/) 

the  subscripts  /  simply  indicating  that  the  air  and  the  gas,  the 
weight  of  which  is  required,  are  at  the  same  temperature. 

The  specific  volume  of  a  gas,  usually  designated  by  the  symbol 
V,  or  the  cubic  feet  per  pound,  will  obviously  be  the  reciprocal  of 
its  specific  weight,  or 


While  it  is  perhaps  easier  and  more  convenient  to  compute 
weight  and  volumetric  data  of  gases  from  their  relative  densities 
and  a  table  of  weights  and  volumes  of  air,  such  values  may  be 
computed  from  the  characteristic  equation  of  a  perfect  gas,  viz  : 

PV=RT  (J) 

where  P=  absolute  pressure  in  pounds  per  square  feet, 
V=volume  per  pound  in  cubic  feet, 
T=absolute  temperature, 

R=a  constant  varying  with  the  gas  and  derived  from  the 
relations  existing  between  the  pressure,  volume  and 
temperature  of  the  gas  in  question. 

15 


This   pressure-volume-temperature  relation   for  any  gas,  as 
indicated  by  the  constant  R,  represents  the  expression 


where  the  subscripts  0  represent  a  set  of  standard  conditions. 
Since  the  volume  (and  hence  the  specific  weight)  of  a  gas  is  a 
function  of  both  temperature  and  pressure,  it  is  necessary,  in 
order  that  there  may  be  a  suitable  basis  for  comparison,  that 
all  volumes  be  reduced  to  some  such  standard  set  of  conditions. 
These  conditions,  as  ordinarily  accepted,  are  a  pressure  of 
14.6963  pounds  per  square  inch  (21 16.27  pounds  per  square  foot) 
and  a  temperature  of  32  degrees  Fahrenheit. 

Table  4  gives  the  weights  and  volumes  of  air  at  atmospheric 
pressure  and  different  temperatures. 

TABLE  4 
VOLUME   AND  WEIGHT  OF  AIR 

AT  ATMOSPHERIC   PRESSURE 


'5 
-jfi 

•c 

j 

i! 
11 

6  °  ^ 

O.QJS 

£**« 

SI 

ill 

||| 

Ml 

II 

JJps, 

||3 

|l| 

II 

III 

i1 

III 

II* 

III 

f|* 

e 

0 

0 

32 

12.390 

.0807  10 

160 

I5-6I5 

.064041 

340 

20.151 

.049625 

50 

12.843 

.077863 

170 

I5.867 

.063024 

360 

20.655 

.048414 

55 

12.969 

.077107 

1  80 

I6.II9 

.062039 

380 

21.159 

.047261 

60 

13.095 

.076365 

190 

16.371 

.061084 

400 

21.663 

.046162 

65 

13.221 

.075637 

200 

16.623 

.060158 

425 

22.293 

.044857 

70 

13-347 

.074923 

210 

16.875 

.059259 

450 

22.923 

.043624 

75 

13-473 

.074223 

212 

16.925 

.059084 

475 

23-554 

.042456 

80 

13-599 

.073535 

220 

17.127 

•058388 

500 

24.184 

.041350 

85 

13-725 

.072860 

230 

17-379 

.057541 

525 

24.814 

.040300 

90 

13-851 

.072197 

240 

17.631 

.056718 

550 

25-444 

.039302 

95 

13-977 

.071546 

250 

17-883 

.055919 

575 

26.074 

.038352 

100 

14.103 

.070907 

260 

18.135 

.055142 

600 

26.704 

.037448 

no 

14-355 

.069662 

270 

18.387 

.054386 

650 

27.964 

.035760 

1  20 

14.607 

.068460 

280 

18.639 

•053651 

700 

29.224 

.034219 

130 

14.859 

.067299 

200 

18.891 

•052935 

750 

30.484 

.032804 

140 

15.111 

.066177 

300 

I9-I43 

.052238 

800 

3x-744 

.031502 

150 

15-363 

.065092 

320 

19.647 

.050898 

850 

33-004 

.030299 

With  the  values  of  P0  and  T0  thus  fixed  (see  absolute 
temperature,  below)  the  value  of  the  constant  R  for  any  gas  as 
given  in  formula  (j-a)  may  be  expressed  as 

2116.27     TT  ,    .. 

R= — /—  V0=4.3045  V0  (3-*>) 

459.64  +  32 

thus  offering  a  means  of  determining  the  value  of  R  directly 
from  the  specific  volume  of  the  gas.  Since  the  specific  volume 
of  a  gas  is  the  reciprocal  of  the  weight  per  cubic  foot,  and  for 
any  two  gases  the  weights  per  cubic  foot  vary  directly  as  their 
molecular  weights,  where  the  value  of  R  for  any  gas  is  known, 
the  value  for  any  other  gas  may  thus  be  determined  from  the 
relations  of  the  molecular  weights  of  the  two  gases,  viz: 

N  3 — Molecular  Weight =2  8  R=  55.13 

Oa — Molecular  Weight=32  R=x 

55.13   :  x  ::  32  :  28 
R  (02)=48.24 

From  the  value  of  R  as  given  in  formula  (j-b)  it  is  possible 
to  express  the  characteristic  equation  of  a  perfect  gas  in  what  is 
perhaps  a  more  convenient  form  for  general  use,  as 

PV_POVO 

T   "        T  v£*J 

1o 

From  the  characteristic  equation  (j),  of  a  perfect  gas,  it  is 
obvious  that  the  volume  of  a  gas  will  vary  inversely  as  the  abso- 
lute pressure  and  directly  as  the  absolute  temperature.  In 
combustion  work  the  variation  in  the  pressure  of  the  gases 
encountered  is  small.  The  temperature  range  covered,  however, 
is  large,  and  because  of  the  effect  of  temperature  change  on 
volume,  it  is  perhaps  well  to  define  here  "absolute  temperature." 

Experiment  shows  that  if  the  temperature  of  a  perfect  gas  at 
32  degrees  Fahrenheit  is  increased  one  degree,  the  pressure  being 
kept  constant,  the  gas  expands  4-~^  part  of  its  volume.  If  such  a 
rate  of  expansion  per  one  degree  increase  in  temperature  held  good 
at  all  temperatures,  and  experiment  shows  that  such  is  the  case 
above  32  degrees,  if  its  pressure  is  kept  constant,  the  gas  would 
double  in  volume  with  an  increase  in  temperature  above  32  degrees 
of  491.64  degrees  Fahrenheit.  Under  a  reduction  of  tempera- 
ture of  491.64  degrees  below  32  degrees  (corresponding  to  an 

17 


ultimate  temperature  of  49 1.64 — 32=459.64  degrees  Fahrenheit 
below  zero)  the  gas  would  disappear.  While  undoubtedly  some 
change  in  the  law  would  occur  before  the  lower  temperature  could 
be  reached,  there  is  no  reason  why  the  law  may  not  be  used  over 
the  temperature  range  in  which  it  is  known  to  hold. 

Table  5  gives  the  densities,  weights  and  volumes  under 
standard  conditions,  of  the  gases  encountered  ordinarily  in 
combustion  problems,  as  well  as  the  values  of  the  constant  R. 

TABLE   5 
DENSITY,  WEIGHT  AND  VOLUME  OF  GASES 

AT  ATMOSPHERIC  PRESSURE  AND  32  DEGREES  FAHRENHEIT 


Substance 

Molecular 
Symbol 

Relative  Density 

Weight 
per 
Cubic  Foot 
Pounds 

Cubic  Foot 
per 
Pound 
Cubic  Foot 

Value  of 
ConstantR 
in 
PV=RT 

Air=i 

Hydrogen=i* 

Air      

1.  0000 

. 

.08071 

12.390 

53-33 

Oxygen    .... 

02 

1-1053 

16 

.08921 

11.209 

48.24 

Hydrogen    .     .     . 

H2 

0.0696 

i 

.00562 

177.936 

765.8 

Nitrogen      .     .     . 

N2 

0.9673 

H 

.07807 

12.809 

55-13 

Carbon  Monoxide 

CO 

0.9672 

M 

.07806 

I2.8II 

55-!5 

Carbon  Dioxide   . 

CO2 

1.5291 

22 

.12341 

8.103 

34.88 

Methane.     .     .     . 

CH4 

0.5576 

8 

.04500 

22.222 

95.64 

Acetylene    .     .     . 

C2H2 

0.9200 

*3 

.07425 

I3.468 

57-97 

Ethylene      .     .     . 

C2H4 

0.9674 

H 

.07808 

12.807 

55-12 

Ethane    .... 

C2H6 

1.0494 

15 

.08470 

1  1.  806 

50.81 

Sulphur  Dioxide  . 

SO2 

2.2639 

32 

.18272 

5473 

2356 

Carbonf  J    .     .     . 

c 

IAC 

0069 

Sulphur  .... 

S2 

125 

.0080 

.•    •    • 

*Based  on  approximate  molecular  weights. 

t Solid.     See  footnote  to  table  i,  page  10. 

JIf  carbon  can  be  conceived  to  exist  as  a  gas  under  standard  conditions  its  relative 
density  would  be  0.820,  its  weight  per  cubic  foot  .0668  pounds,  and  its  volume  14.97  cubic 
feet  per  pound. 

From  the  foregoing  it  is  evident  that  under  a  constant  pres- 
sure, the  volume  of  a  gas  will  vary  directly  as  the  number  of 
degrees  between  its  temperature  and  the  temperature  — 459.64 
degrees  Fahrenheit.  To  simplify  the  application  of  the  law,  a 
new  thermometric  scale  is  constructed,  the  point  corresponding 
to  — 460  degrees  Fahrenheit  being  taken  as  the  zero  point,  and 
the  degrees  being  of  the  same  magnitude  as  those  on  the  Fah- 
renheit scale.  Temperatures  referred  to  this  new  scale  are  called 


18 


absolute  temperatures,  and  its  zero  point  ( — 460  degrees  Fahren- 
heit) absolute  zero.  The  Fahrenheit  scale  is  converted  to  the 
absolute  scale  simply  by  adding  460  degrees  to  the  Fahrenheit 
reading. 

Since  the  volume  of  a  gas  at  constant  pressure  varies  as  the 
absolute  temperature,  if  one  pound  of  gas  is  at  a  temperature  of 
60  degrees  Fahrenheit  and  a  second  pound  at  500  degrees  Fah- 
renheit, the  respective  volumes  at  a  given  pressure  would  be  in 
the  ratio  of  60+460=520  to  500+460=960. 

In  combustion  work,  gas  analyses  are  frequently  given  in 
terms  of  volume  when  analyses  in  terms  of  weight  are  required. 
To  convert  a  volumetric  analysis  to  one  by  weight,  the  percentage 
by  volume  of  each  constituent  gas  should  be  multiplied  by  its 
relative  density,  each  product  being  divided  by  the  sum  of  the 
products.  To  convert  an  analysis  bv  wfijyh*  *f*-ar\+  fa  t*r*n*  *f 
volume,  the  percentage  by  weight  of  each  constituent  should  be 
divided  by  its  relative  density,  and  each  quotient  so  obtained 
be  divided  by  the  sum  of  the  quotients.  Since  the  molecular 
weights  of  the  various  gases  bear  the  same  relations  to  each 
other  as  the  relative  densities,  these  molecular  weights  may  be 
used  in  transforming  analyses  instead  of  the  relative  densities. 

Another  method  of  converting  volumetric  analyses  to  analyses 
in  terms  of  percentage  by  weight  is  through  the  use  of  the 
weights  per  cubic  foot  of  the  various  constituent  gases.  The. per- 
centages by  volume  are  multiplied  by  the  weights  per  cubic  foot, 
and  each  product  is  divided  by  the  sum  of  the  products.  This 
method  has  an  advantage  in  that  it  gives  directly,  in  the  sum  of 
the  products,  the  weight  of  the  gas  as  a  whole  per  cubic  foot. 


HEAT  OF  COMBUSTION 

WHEN  elements  enter  into  a  direct  combination  to 
form  a  compound  a  definite  amount  of  heat  is  either 
evolved  or  absorbed.     Such  amount  of  heat  is  called 
the  heat  of  combination  and  from  its  very  definition  may  be 
either  positive  or  negative.  When  a  compound  is  decomposed 
into  its  constituent  elements  the  amount  of  heat  absorbed  or 
evolved  is  exactly  the  same  as  that  which  was  evolved  or  absorbed 
in  the  original  formation  of  the  compound.    When  both  combina- 
tion and  decomposition  are  involved  in  a  complex  chemical  change 
the  heat  produced  or  absorbed  is  the  net  result  of  the  two  reactions. 

HEAT  OF  COMBUSTION 

Since  the  term  combustion,  as  used  in  furnace  practise,  is 
limited  to  the  rapid  chemical  combination  of  the  combustible 
constituents  of  a  fuel  and  oxygen,  with  a  resulting  production 
of  heat,  the  heat  of  combustion  of  a  fuel  is  obviously  the  heat 
evolved  in  the  complete  oxidization  of  such  combustible  elements 
through  union  with  oxygen.  The  heat  of  combustion  is  thus 
the  heat  of  combination  of  a  specific  set  of  elements  and 
compounds,  the  combination  of  which  with  oxygen  always 
results  in  the  production  of  heat.  It  follows  that  the  heat  of 
combination  of  a  compound  which  results  from  the  union 
of  a  single  combustible  element  with  oxygen  to  produce  heat  is 
the  same  as  the  heat  of  combustion  of  that  element. 

The  principles  controlling  the  development  of  heat  by 
combustion  as  generally  accepted  as  authoritative  are  those 
propounded  by  Berthelot.  His  "second  law"  is  of  particular 
interest  in  combustion  as  limited  to  furnace  practise,  and  as 
applied  to  such  practise  may  be  stated  as  follows : 

The  heat  energy  evolved  in  any  chemical  change  in  the 
boiler  furnace,  where  no  mechanical  work  is  done,  i.  e.,  evolved 
through  the  union  of  combustible  elements  with  oxygen,  is  de- 
pendent upon  the  final  products  of  combustion  and  in  no  way 
upon  any  intermediate  combination  or  combinations  that  may 
have  occurred  in  reaching  the  final  result. 

The  application  of  this  law  may  be  readily  shown  by  example  : 

A  coal  fire  from  which  all  of  the  volatile  constituents  have 
been  driven  and  which  consists  of  incandescent  coke  may  for 


20 


the  present  purpose  be  considered  as  consisting  entirely  of 
carbon.  If  air  is  introduced  under  the  fire  the  oxygen  immedi- 
ately breaks  its  mechanical  union  with  nitrogen  and  enters  into 
chemical  combination  with  carbon  to  form  carbon  dioxide 
(C+2  O  =  CO2).  Each  unit  of  carbon  has  combined  with  the 
maximum  amount  of  oxygen  with  which  it  can  exist  as  a  com- 
pound. The  oxygen  on  the  other  hand  is  capable  of  uniting  with 
additional  carbon  and  as  the  unit  of  carbon  dioxide  passes  upward 
through  the  fuel  bed  under  the  influence  of  draft  it  encounters 
other  free  carbon  with  which  it  unites  to  form  carbon  monoxide 
(CO2  +  C  =  2CO),  thus  "satisfying  the  affinity  of  oxygen  for 
carbon."  If  no  additional  oxygen  is  encountered  in  the  further 
passage  through  the  fuel  bed,  these  particular  molecules,  as 
representative  of  the  products  of  combustion,  will  issue  from  the 
fuel  bed  as  carbon  monoxide.  If  no  additional  oxygen  is  encoun- 
tered in  the  furnace  the  total  heat  available  for  later  absorption 
by  the  boiler  is  that  due  to  the  combustion  of  carbon  to  carbon 
monoxide  regardless  of  the  fact  that  at  one  stage  of  the  process 
the  carbon  had  been  completely  oxidized  and  carbon  dioxide 
had  been  produced.  If,  on  the  other  hand,  additional  oxygen  is 
encountered  in  the  furnace,  the  temperature  is  above  the  ignition 
point  of  carbon  monoxide,  and  this  temperature  is  maintained  a 
sufficient  length  of  time  for  further  combustion,  i.  e.t  if  the  gases 
are  not  cooled  below  the  ignition  temperature  by  the  boiler 
heating  surface  before  further  combustion  can  be  completed, 
the  carbon  of  the  carbon  monoxide  will  unite  with  additional 
oxygen  to  form  carbon  dioxide  (2CO+2  O  =  2CO2).  The  total 
heat  evolved  and  available  for  absorption  in  such  cases  will  be 
that  due  to  the  burning  of  carbon  to  carbon  dioxide  regardless  of 
the  two  intermediate  steps. 

That  combustible  substances  exist  is,  under  the  laws  of 
chemical  combination,  an  absolute  indication  that  at  some  time 
there  was  expended  an  amount  of  energy  in  some  transformable 
shape  equivalent  to  the  heat  of  combustion  of  the  individual 
substance  considered.  While  it  is  not  within  the  province 
of  the  present  article  to  discuss  the  reactions  which  brought 
about  the  state  of  existence  of  the  combustible  substances 
as  used  for  ordinary  heat  generation,  the  above  statement 
may  be  accepted  as  true  and  the  principles  involved  simply 


21 


as  being  of  the  general  laws  covering  the  conservation  of  energy. 
The  heat  of  combustion  of  a  fuel,  or  as  it  is  sometimes  called, 
the  calorific  value,  as  used  in  boiler  practise,  is  the  amount  of 
heat  expressed  in  B.  t.  u.  generated  by  the  complete  combustion 
or  oxidization  of  one  pound  of  the  fuel  in  question.  The  amount 
of  heat  so  generated  is  a  constant  for  any  given  combination  of 
combustible  elements  and  compounds,  and  in  accordance  with 
Berthelot's  second  law  is  irrespective  of  the  manner  in  which 
combustion  takes  place,  so  long  as  it  is  complete. 

The  unit  of  measure  of  quantity  of  heat  is,  as  stated  above, 
the  B.  t.  u.  Until  recently  this  has  ordinarily  been  defined  as 
the  amount  of  heat  necessary  to  raise  the  temperature  of  one 
pound  of  water  at  a  definite  temperature,  one  degree  Fahrenheit. 
The  value  as  now  generally  accepted  is  T!<jth  of  the  amount  of 
heat  necessary  to  raise  the  temperature  of  one  pound  of  water 
from  32  degrees  to  212  degrees  Fahrenheit. 

Table  6  gives  the  heat  of  combustion  of  what  may  be  termed 
the  ""pure  fuels" whether  elements  or  compounds.  These  are  found 
in  various  combinations  in  the  fuels  encountered  in  boiler  practise. 

TABLE  6* 
HEAT  OF  COMBUSTION 

BY   CALORIMETRIC   DETERMINATION 


Heat  Value  —  B.  t.  u.  per  Pound 

Per  Cubic  Foot  J 

Combustible 

Molecular 
Symbol 

Higher 

Lower  or  Nett 

Higher 

Hydrogen.     .     .     . 

H2 

62OOO 

52920 

348 

Carbon  (to  CO)  .    . 

C 

4380 

. 

.     .     . 

Carbon  (to  CO2)  . 

C 

14540 

.     .     . 

.      .     . 

Carbon  Monoxide  . 

CO 

4380 

342 

Carbon  in  CO  §  .     . 

C 

IOl6o 

.      .     . 

.     .     . 

Methane   .... 

CH4 

23850 

21670 

1073 

Acetylene.    .     .     . 

C2H2 

21460 

2IO2O 

1590 

Ethylene  .... 

C2H4 

21450 

20420 

1675 

Ethane      .... 

C2H6 

22230 

20500 

1883 

Sulphur  (to  SO2)    . 

S2 

4050 

•      •      . 

-     •     • 

Sulphur  (to  SO3)    . 

S2 

5940 

•      •      • 

•     •     ' 

t  There  is  a  considerable  discrepancy  between  lower  heat  values  as  given  by  different 
authorities,  the  variation  being  due  to  methods  of  computation  and  assumptions.  (See  text.) 
The  values  given  are  those  of  G.  A.  Goodenough. 

J  At  32  degrees  Fahrenheit  and  atmospheric  pressure. 

§  Per  pound  of  carbon  in  carbon  monoxide,  t.  £.,  2.33  pounds  of  CO. 

*  Heating  Value  by  Calorimetry,  see  Discussion,  page  23. 


22 


It  appears  from  Table  6  that  when  one  pound  of  carbon  is 
burned  to  carbon  monoxide  the  heat  produced  is  10, 160  B.  t.  u. 
less  than  if  the  carbon  were  completely  oxidized  or  burned  to 
carbon  dioxide.  That  such  a  difference  exists  in  the  amount  of 
heat  evolved  in  the  burning  of  a  fuel  in  two  different  ways  offers 
the  possible  source  of  one  of  the  most  prolific  of  furnace  losses. 
This  will  be  discussed  at  greater  length  in  connection  with 
air  supply  and  combustion. 

The  heat  of  combustion  of  a  fuel  is  the  basis  upon  which  the 
efficiency  of  a  steam  boiler  is  computed  and  is  therefore  of  the 
greatest  importance. 

MEASUREMENT  OF  HEAT  OF  COMBUSTION 

The  most  satisfactory  method  of  determining  the  heat  value 
of  any  fuel  is  by  the  direct  measurement  of  the  heat  evolved 
during  combustion  in  a  calorimeter.  Descriptions  of  fuel  calori- 
meters and  the  methods  of  their  operation  are  given  by  numerous 
authorities  and  need  no  discussion  here. 

For  solid  fuels  and  most  liquid  fuels,  calorimeters  of  the 
"bomb"  type  in  which  combustible  substances  are  burned  in  a 
constant  volume  of  oxygen,  give  the  most  satisfactory  results. 
With  such  calorimeters,  properly  operated,  combustion  will  be 
complete,  all  of  the  heat  generated  will  be  absorbed  and  measured, 
and  heat  from  external  sources  can  either  be  excluded  or  have 
proper  correction  made  for  its  presence. 

For  gaseous  fuels  calorimeters  of  the  continuous  or  constant 
flow  type  are  ordinarily  used,  the  Junker  calorimeter  being  ac- 
cepted as  standard  for  this  class  of  work. 

The  accuracy  of  the  determination  of  the  heat  value  of  a  fuel 
by  calorimetry  is  largely  a  question  of  the  personal  equation ;  the 
more  careful  the  manipulation  of  the  instrument  the  more  accurate 
will  be  the  results.  With  careful  manipulation,  the  results  should 
be  accurate  to  within  a  fraction  of  one  per  cent. 

For  solid  and  liquid  fuels  separate  determinations  are  necessary 
for  the  heat  value  of  each  specific  fuel.  For  elements  and  com- 
bustible compounds  entering  into  gaseous  fuels  the  heats  of 
combustion  have  been  determined  by  so  many  authorities  that 
definite  values  may  be  accepted  as  correct  without  determination. 
In  view  of  the  difficulties  of  computing  the  heat  values  of  such 
combustibles  this  fact  is  fortunate. 


23 


COMPUTATION  OF  HEAT  OF  COMBUSTION 

While  the  heat  value  of  a  fuel  may,  as  stated,  be  most  satis- 
factorily determined  by  actual  experiment  in  a  calorimeter,  it 
frequently  happens  that  such  apparatus  is  not  available.  Under 
such  conditions  approximate  heat  values  may  be  determined  for 
certain  fuels  by  computation  from  the  ultimate  chemical  analysis 
of  the  fuel.  The  formula  for  such  computation  in  most  general 
use  and  which  for  most  coals  gives  reasonably  accurate  results  is 
that  of  Dulong.  This  formula,  using  approximate  figures,  is 

B.t.u.  per  pound— 14,600  C  +  62,000  (H — --)+4O5oS  (4) 

8 

the  symbols  representing  the  proportionate  parts  by  weight  of 
carbon,  hydrogen,  oxygen  and  sulphur  in  the  fuel,  while  the  co- 
efficients represent  the  approximate  heating  values  of  the 
constituents  with  which  they  appear  in  the  formula.  The  term 

(H — —)  is  assumed  to  contain  a  correction  for  the  hydrogen  in 
8 

the  fuel  which  is  combined  with  oxygen  and  exists  as  moisture. 
Dulong's  formula  will  give,  as  stated,  very  close  approximations 
for  the  heat  value  of  most  coals — probably  within  2  or  3  per 
cent.  There  are,  however,  certain  sources  of  possible  error 
in  the  use  of  the  formula  even  for  the  fuels  with  which  it 
gives  the  most  accurate  results,  and  since  these  sources  of 
error  offer  the  explanation  of  why  the  formula  is  not  applicable 
to  all  fuels,  and  particularly  to  gaseous  fuels,  their  discussion 
seems  warranted. 

(a)  Carbon  and  sulphur  are  the  only  elements  in  coal  in  a 
free   state,  but   a  portion  of  these  constituents  may  occur  in 
elementary  form.     The  carbon  may  be  present  as  graphite  or  as 
amorphous   carbon,  the  heating  values  of   which  are  entirely 
different.     The  sulphur  may  exist  as  FeS2  (pyrites).     Further, 
the  sulphur  may  be  burned  to  SO2  or  SO3,  in  the  production  of 
which  the  amount  of  heat  evolved  is  widely  different.      (See 
Table  6.) 

(b)  If  portions  of  the  carbon  and  hydrogen  are  combined  as 
hydrocarbons,  the   heating   value  of   such  combinations  is  far 
different  than  if  the  elements  existed  separately,  since  in  such 
case  the  heat  of  combination  or  of  dissociation  would  have  to  be 


considered.  This  factor  makes  questionable  the  heat  value  of  a 
portion  of  the  carbon  and  probably  of  all  of  the  hydrogen. 

(c)  The  term  (H — — )  which  is  assumed  to  be  correct  for  that 

o 

portion  of  hydrogen  contained  in  the  moisture  is  not  a  proper 
assumption,  since  a  portion  of  the  oxygen  unquestionably  exists 
in  a  free  state  in  all  fuels. 

(d)  An  additional  portion  of  the  oxygen  is  in  all  probability 
combined  with  nitrogen  in  certain  organic  nitrates  and  some  may 
possibly  exist  in  combination  as  carbonates  in  mineral  matter 
foreign  to  the  coal. 

All  of  these  factors  tend  toward  error.  While  with  most  coals 
the  error  is  small,  it  is  unfortunately,  with  the  generally  accepted 
co-efficients,  one  of  excess.  In  the  case  of  gaseous  fuels,  however, 
in  view  particularly  of  items  (b)  and  (c)  above,  the  chance  of  error 
is  great.  The  magnitude  of  error  will  depend  in  such  cases  upon 
the  individual  set  of  hydrocarbons  present  in  the  fuel.  If  we  had, 
for  instance,  a  fuel  composed  of  C5H6O2,  the  constituents  might 
be  united  in  such  a  number  of  different  combinations  as  to  give 
results  varying  with  the  manner  of  combination,  from  2.3  per  cent 
less  to  14.7  per  cent  greater  than  the  result  which  would  be  ob- 
tained from  the  application  of  Dulong's  formula,  which  assumes 
that  all  of  the  oxygen  is  combined  with  hydrogen  as  water. 

Numerous  other  formulae  of  an  empirical  nature  for  the 
determination  of  the  heat  value  of  fuels  have  been  offered  by 
various  authorities.  Most  of  these  are  based  upon  a  series  of 
chemical  analyses,  and  while  they  give  reasonably  accurate  results 
in  the  case  of  individual  classes  of  coal,  they  fail  when  an  attempt 
is  made  to  apply  them  not  only  to  other  classes  of  fuel,  but  even 
to  other  classes  of  coal. 

The  only  accurate  and  reliable  heating  value  of  a  fuel  is  that 
determined  experimentally  with  a  calorimeter,  and  such  determi- 
nation should  correctly  be  reported  as  a  part  of  the  ultimate  or 
proximate  chemical  analysis  of  the  fuel. 

In  the  case  of  the  usual  gases  where  the  proportionate  parts 
by  weight  may  be  readily  determined,  the  heating  value  may  be 
accurately  computed  from  a  table  of  the  heat  values  of  individual 
constituents,  which  values  have  been  definitely  fixed  by  numerous 
calorimetric  experiments. 


HIGHER  AND  LOWER  HEAT  VALUES 

The  heat  value  of  a  fuel  as  defined  is  known  as  the  "higher" 
heat  value  and  is  ordinarily  accepted  as  the  standard  in  this 
country.  In  the  case  of  fuel  containing  hydrogen,  and  this 
includes  practically  all  fuels  in  commercial  use,  there  is  another 
value  known  as  the  "lower,"  "net"  or  "available"  heat  value, 
in  the  determination  of  which  an  attempt  is  made  to  allow  for  the 
latent  heat  recovered  in  the  condensation  of  the  water  vapor 
formed  in  the  combustion  of  hydrogen.  For  example :  In  the 
calorimetric  determination  of  the  heat  value  of  a  fuel  containing 
hydrogen,  the  products  of  combustion  are  cooled  to  approximately 
the  temperature  of  the  original  mixture,  say  62  degrees  Fahren- 
heit. In  cooling  the  products  to  this  temperature  the  water  vapor 
formed  by  the  combustion  of  hydrogen  is  condensed,  and  the 
result,-  expressed  in  B.  t.  u.,  after  being  corrected  for  sulphur  and 
like  factors,  i.  e.,  the  higher  heat  value,  includes  the  latent  heat 
of  water  vapor  given  up  in  such  condensation. 

If  the  lower  value  be  represented  by  H/  and  the  weight  of 
water  produced  per  pound  of  fuel  by  wt  the  lower  heat  value  may 

be  determined  from         t,  t     „ 

H/=H>— wr  (S) 

where  H^  equals  the  higher  heat  value  and  r  is  a  factor  which 
varies  with  the  percentage  of  hydrogen  in  the  fuel,  the  amount 
of  air  or  oxygen  used  in  combustion,  the  moisture  in  the  air  and 
the  temperature  to  which  the  products  of  combustion  are  cooled 
in  the  calorimeter.  Too  frequently  r  is  simply  taken  as  the  latent 
heat  of  steam  either  at  32  degrees  or  2 12  degrees,  though  in  calori- 
metric work  neither  of  these  temperatures  are  apt  to  occur. 

With  the  lower  heat  value  so  defined,  the  difference  between 
the  higher  and  the  net  value  will  obviously  be  the  total  heat  of 
the  steam  or  water  vapor  as  it  escapes  less  the  sensible  heat  of 
an  equivalent  weight  of  water  at  the  temperature  of  the  fuel  and 
of  the  oxygen  before  combustion  takes  place. 

The  lower  heat  value  is  in  common  use  in  Great  Britain  and 
in  most  foreign  countries.  In  this  country  the  higher  value  is 
almost  universally  accepted,  and  this  is  the  standard  recommended 
by  the  American  Society  of  Mechanical  Engineers. 

Any  attempt  to  make  use  of  the  lower  heat  value  introduces 
a  source  of  possible  error  in  the  proper  temperature  for  use  in 

26 


computation,  and  advocates  of  the  use  of  this  value  are  not  in 
entire  agreement  as  to  the  proper  methods  of  such  computations. 
To  sum  up,  a  theoretically  perfect  absorption  of  heat  after 
combustion  would  condense  all  of  the  moisture  formed  in  the 
burning  of  hydrogen,  and  since  the  efficiency  of  any  apparatus  is 
based  upon  the  performance  of  a  theoretically  perfect  machine,  it 
appears  only  logical  to  charge  against  the  apparatus  what  would 
be  secured  from  the  theoretically  perfect.  Further,  in  the  report 
of  the  performance  of  any  apparatus,  a  heat  balance  offers  a 
method  of  determining  and  expressing  any  loss  due  to  the  burn- 
ing of  hydrogen,  and  no  such  test  or  performance  report  can  be 
accepted  as  reliable  unless  accompanied  by  a  heat  balance  or  by 
data  from  which  a  heat  balance  may  be  computed. 


27 


SPECIFIC  HEAT 

THE  heat  of  combustion  of  any  substance  from  its  very 
nature  must  have  an  important  bearing  on  the  temperature 
which  will  result  from  the  burning  of  such  substance. 
Before  discussing  the  temperatures  so  developed,  a  knowledge  of 
the  specific  heats  is  necessary.  This  subject  is  important  in  the 
computation  of  many  combustion  data,  and  for  this  reason  is 
considered  at  length. 

The  specific  heat  of  a  substance  is  the  amount  of  heat 
expressed  in  thermal  units  required  to  raise  unit  weight  of  the 
substance  through  one  degree  of  temperature,  the  units  in  this 
country  being  one  pound  and  one  degree  Fahrenheit. 

The  specific  heat  of  all  substances  varies  with  the  temperature. 
Since  all  substances  vary  in  volume  or  in  pressure  with  changes 
in  temperature,  it  is  necessary  to  distinguish  between  the  specific 
heats  at  constant  volume  and  at  constant  pressure,  expressed 
ordinarily  as  Cv  and  C^,  respectively. 

Liquids  and  solids,  because  of  their  low  co- efficients  of 
expansion,  vary  but  little  in  volume  under  a  temperature  change 
of  one  degree  and  for  these  substances  therefore  there  is  but  little 
difference  in  the  specific  heat  at  constant  volume  and  that  at 
constant  pressure.  With  gases,  on  the  other  hand,  there  is  a 
decided  distinction.  When  any  heat  is  added  to  a  gaseous 
substance,  its  volume  may  be  kept  constant,  in  which  case  no 
external  work  is  done,  or  the  gas  may  be  allowed  to  expand  during 
the  addition  of  heat,  the  pressure  being  kept  constant.  The 
specific  heat  at  constant  volume  therefore  will  always  be  less  than 
that  at  constant  pressure  by  the  amount  of  heat  required  to  do 
the  work  of  expansion  against  external  pressure. 

Under  both  specific  heat  at  constant  pressure  and  that  at 
constant  volume  it  is  necessary  to  distinguish  still  further  between 
instantaneous  and  mean  specific  heat. 

The  instantaneous  specific  heat  of  a  substance  is  the  amount 
of  heat  that  must  be  added  to  a  unit  weight  of  such  substance  at 
some  definite  temperature  to  increase  its  temperature  one  degree, 
under  given  conditions  of  pressure  or  volume. 

The  mean  specific  heat  of  a  substance,  over  a  given  tempera- 
ture range,  is  the  value  by  which  such  range  must  be  multiplied 

28 


to  determine  the  quantity  of  heat  necessary  to  raise  unit  weight 
of  the  substance  through  the  range  under  the  conditions  of 
pressure  or  volume  which  exist. 

In  the  computation  of  combustion  data  the  mean  specific  heat 
should  be  used. 

From  the  definition  of  a  B.  t.  u.  as  hitherto  accepted  (see 
page  22),  when  the  specific  heat  of  water  is  given  as  unity,  such 
value  would  express  the  instantaneous  specific  heat  at  constant 
pressure,  at  the  standard  temperature  (usually  62  degrees  Fahren- 
heit). From  the  definition  now  accepted — namely,  TiTjth  of  the 
heat  required  to  raise  one  pound  of  water  from  32  degrees  to 
212  degrees  Fahrenheit — where  the  specific  heat  is  given  as  one, 
such  value  is  the  mean  specific  heat  between  32  and  212  degrees. 

Except  in  the  case  of  water  vapor,  the  variation  with  pressure 
in  the  specific  heat  of  the  gases  ordinarily  encountered  in  com- 
bustion work  is  negligible.  In  the  case  of  water  vapor,  where  it 
is  necessary  to  deal  with  any  considerable  range  of  pressures, 
this  variation  would  be  an  appreciable  factor,  but  in  the  usual 
gases  involved  in  combustion,  the  partial  pressure  exerted  by 
water  vapor,  either  in  gases  before  combustion  or  in  the  exhaust 
gases,  is  rarely  over  one  pound  absolute.  With  such  a  limited 
pressure  range  and  in  view  of  the  fact  that  the  water  vapor 
content  of  the  gases  is  small,  the  effect  of  such  variation  in 
pressure  on  the  specific  heat  of  the  gas  as  a  whole  may  be 
neglected. 

The  range  of  pressure  in  the  gases  encountered  in  boiler  work 
is  so  limited — varying  from  that  at  which  the  ordinary  gases 
are  introduced  into  the  furnace  for  combustion  to  the  suction 
under  which  they  are  drawn  over  the  boiler  heating  surfaces — that 
in  the  computation  of  combustion  data  the  gases  may  be  safely 
assumed  to  be  at  a  constant  pressure.  The  specific  heat  at 
constant  pressure  is  the  specific  heat  which  should  be  used,  and 
any  results  based  on  the  assumption  of  a  constant  pressure  of  the 
gases  as  a  whole,  and  in  which  the  variation  in  the  specific  heat  of 
the  water  vapor  content  with  change  of  pressure  is  neglected, 
will  be  well  within  the  limits  of  accuracy  of  practically  all  com- 
bustion data  computation. 

While  the  variation  in  specific  heat  with  pressure  can  be 
neglected,  the  variation  with  temperature  is  a  very  appreciable 

29 


factor  and  must  be  given  proper  consideration  where  accuracy 
is  desired. 

The  results  of  the  great  amount  of  experimental  work  that 
has  been  done  in  the  determination  of  the  specific  heat  of  gases 
are  unfortunately  not  in  complete  agreement.  From  the  work 
of  Holborn  and  Henning,  Langen,  Pier  and  Austin,  however,  the 
specific  heats  of  the  diatomic  gases  (H2,  O2,  N2  and  CO)  and  of 
carbon  dioxide  and  water  vapor  are  pretty  definitely  determined. 
The  values  for  these  gases  which  follow  are  apparently  the  most 
authoritative  of  those  that  have  been  offered. 

The  general  formula  for  the  specific  heat  of  a  gas  at  constant 
pressure  may  be  expressed  by  the  function 

The  mean  specific  heat  of  a  gas  between  the  temperatures 
tl  and  £2  will  be  then 

_  rt,   a+bt+ct*+dt* 

Isp I        J.  Ul 

or  by  integration 


4  x 

CARBON  DIOXIDE 

The  value  of  the  instantaneous  specific  heat  at  constant 
pressure  of  CO2,  as  given  by  Holborn  and  Henning,  in  terms  of 
the  Fahrenheit  scale  is 

£,,=0.1983  +  835  x  io-V — 16.7  x  io~9/2         (8) 

Values  as  determined  by  this  formula  decrease  rapidly  at 
temperatures  above  2400  degrees  Fahrenheit.  That  such  a 
decrease  occurs  appears  questionable,  and  for  this  reason  it 
seems  advisable  to  modify  the  formula  in  such  a  manner  as  to 
continue  the  increase  in  specific  heat  with  temperature  in  a 
logical  way.  Mathias  Pier  investigated  the  specific  heat  of  CO2 
at  high  temperatures  and  the  values  as  determined  by  him  are 
above  those  of  Holborn  and  Henning.  A  modification  of  Holborn 

30 


and  Henning's  formula  (8)  for  use  in  the  case  of  temperatures 
above  2200  degrees  D.  which  appears  to  give  logical  results  is 

^,—  .1991  +  873  x  icr7/ — 23.4  x  io~9/2  +  o.22x  icr11/3  (9)* 
This  formula  gives  values  for  the  specific  heat  of  CO2  above 
2200  degrees  Fahrenheit  greater  than  those  of  Holborn  and 
Henning  and  somewhat  less  than  those  of  Pier. 

Formula  (8),  which  should  be  used  for  temperatures  up  to 
2200  degrees  Fahrenheit,  in  terms  of  mean  specific  heat  at 
constant  pressure  for  a  temperature  range  o — /,  in  accordance 
with  the  relation  between  instantaneous  and  mean  specific  heats 
as  indicated  by  formulae  (6)  and  (7)  will  become 

^^—0.1983  +  417.5  x  io~7/ — 5.567  x  io~9/2    (10) 
For  a  range  of  definite  temperatures,  t^ — *3,  the  constants  will  be 
the  same  as  in  (id),  the  values  of  t^  and  ta  being  substituted  as 
indicated  in  (7). 

For  temperatures  above  2200  degrees,  the  mean  specific  heat 
at  constant  pressure  between  o  and  t  degrees  Fahrenheit  becomes 
from  formula  (p) 

4^—0.1991+436.5  x  io~7/ — 7-8x  io~9/2+5.5  x  io~13/3  (//) 
and  for  a  temperature  range  t^ — /2,  the  proper  value  may  be  com- 
puted in  accordance  with  values  of  t^  and  /3  indicated  by  (7),  using 
the  constants  as  given  in  (//). 

CARBON    MONOXIDE   AND    NITROGEN 

Holborn  and  Henning  give  the  instantaneous  specific  heat  of 
nitrogen  at  constant  pressure  as 

^=0.2343 +.  00002*1  t  (12} 

Their  investigations  extended  to  a  temperature  of  2456 
degrees  Fahrenheit  and  appear  to  offer  the  most  authoritative 
values.  In  the  absence  of  data  at  higher  temperatures  it  is 
necessary  to  accept  this  formula  for  all  temperatures. 

The  mean  specific  heat  between  o  and  t  becomes  then 

OW=o.2343 +  .0000105  /  (/j) 

and  for  a  range  /t — t^  as  indicated  in  the  case  of  carbon  dioxide. 

Formulae  (12)  and  (ij)  will  also  give  the  specific  heat  of 
carbon  monoxide. 


*  See  "  Experiments  on  the   Rate  of   Heat   Transfer  from  a  Hot  Gas  to  a  Cooler 
Metallic  Surface."     The  Babcock  &  Wilcox  Co.,  1916. 

31 


Mean  Specific  Heat— Water  Vapor 

.55        .54        -53        -52         -51        -5°        -49        -48        47        -46       45 

Mean  Specific  Heat — Hydrogen 
4-1        4-o        39        3-8       3-7        3-6        3-5        34       3-3 


.29         .28  .27  .26  .25  .24  .23  .22  .21  .20  .19 

Mean  Specific  Heat,  Carbon  Monoxide,  Carbon  Dioxide,  Oxygen,  Nitrogen,  Air. 

FIGURE  i 


.3- 


OXYGEN 

The  data  on  the  specific  heat  of  oxygen  are  meagre.  Holborn 
and  Austin  experimented  with  oxygen  mixed  with  9  per  cent 
nitrogen  up  to  temperatures  of  1 1 60  degrees  Fahrenheit,  while 
Langen  and  Pier  investigated  at  higher  temperatures.  The  best 
formula  offered  *  is  apparently  one  which  gives  values  somewhat 
higher  than  those  of  Langen  and  Pier,  but  which  agrees  more 
nearly  in  values  with  that  proposed  by  Holborn  and  Henning. 

This  formula  for  the  instantaneous  specific  heat  of  oxygen  at 

constant  pressure  is 

^=0.2154+0.000019  /  (14) 

and  for  the  mean  specific  heat  over  the  range  o — t 

*A^=o.2 1 54+  .0000095  t  (iS) 

HYDROGEN 

Holborn  and  Henning  give  as  the  mean  molecular  specific 
heat  of  hydrogen 

0*4^=6.58+0.000532  /  (16) 

This  in  terms  of  mean  specific  heat  becomes 

^=3.29  +  0.000266  /  (77) 

WATER  VAPOR 

The  formula  for  the  specific  heat  of  water  vapor  is  based  on 
the  values  given  in  Marks  and  Davis'  Steam  Tables.  This 
formula  for  the  instantaneous  specific  heat  at  a  constant  pressure 
of  one  pound  absolute  (which  may  be  accepted  as  correct  for  the 
partial  pressure  of  the  water  vapor  in  the  gases  of  combustion 
data  work  over  the  range  of  draft  pressure  or  suction  found)  is 

^=0.4541  + 32  X  IO~7/+-2825X  IO'11/2          (18)* 

The  mean  specific  heat  for  the  range  o — t  will  be 

CP^I— 0.4541  +  i6x  io~7/+942  x  IO'11/2       (79) 

For  a  range  of  temperature  tl — /2  this  means  specific  heat 
will  be 


*  See  "Experiments  on  the  Rate  of  Heat  Transfer  from  a  Hot  Gas  to  a  Cooler  Metallic 
Surface."     The  Babcock  &  Wilcox  Co.,  1916. 

33 


The  specific  heat  of  a  gaseous  mixture  is  found  by  multiplying 
the  percentage  by  weight  of  each  of  the  constituent  gases  by  the 
specific  heat  of  that  gas  and  dividing  the  sum  of  the  products 
by  100. 

Investigations  of  the  specific  heats  of  other  important  gases 
encountered  in  combustion  work,  over  any  considerable  tempera- 
ture range  are  lacking,  though  it  is  possible  in  one  or  two 
instances,  to  give  formulae  from  which  approximate  values  may 
be  computed.  In  the  computation  of  combustion  work  such  gases 
(CH4,  C2H4,  etc.)  are  ordinarily  dealt  with  at  atmospheric  or  at 
least  at  low  temperatures,  under  which  conditions  reasonably 
accurate  values  are  available.  Further,  the  percentages  of  such 
gases  in  the  ordinary  gaseous  fuels  are  not  such  as  to  cause  any 
great  error  in  the  determination  of  the  specific  heat  of  the  gas  as 
a  whole  through  the  use  of  inaccurate  or  questionable  specific  heats 
for  these  individual  constituents.  What  appear  to  be  the  most 
authoritative  values  for  the  specific  heats  of  these  gases  at  60 
and  600  degrees  are  given  in  Table  7. 

TABLE  7 

MEAN  SPECIFIC  HEATS  AT  CONSTANT  PRESSURE 
AND  ORDINARY  TEMPERATURES 


Molecular 
Symbol 

Mean  Specific  Heat 

o  —  60  Degrees 
Fahrenheit 

0—600  Degrees 
Fahrenheit 

Air  «*  .    .    . 

02 
H2 
N2 
CO 
C02 
H20 
CH4 
C2H4 
SO2 

.2381 
.2l6o 
3-3850 
•2349 
•2349 
.2008 
•4542 
.498 
•348 
•1544 

.2484 
.2211 

3-475° 
.2406 
.2406 
.2214 
.4586 
.649 
.461 

Hydrogen                    .         . 

Nitrogen  

Carbon  Monoxide  .     .     *    . 
Carbon  Dioxide     .     .    •  •••'•• 
Water  Vapor     .    .    «    .    » 

Methane*.     .    ,    .    •    .    .  ' 

Ethylenet  .     •    ...    .     . 

Sulphur  Dioxide    

*  Methane—  £4^=0.48  1  +0.00028  t 

t 


The  mean  specific  heats  between  o  and  t,  the  gas  temperature, 
of  the  ordinary  gases  encountered  in  combustion  work,  and  of 
water  vapor  are  shown  graphically  in  Figure  I  . 


34 


TEMPERATURES  DEVELOPED  IN 
COMBUSTION 

IF  in  the  burning  of  any  fuel,  it  is  assumed 
First,  that  combustion  is  complete; 
Second,  that  there  is  no  radiation  loss ; 
Third,  that  there  is  no  dissociation ;  and 

Fourth,  that  the  inert  gases  play  no  part  in  the  reaction; 
the  total  heat  generated  must  be  transferred  to  the  products  of 
combustion,  and  raise  their  temperature  above  that  of  the  fuel 
and  the  air  supplied  for  combustion  a  definite  amount,  depending 
upon  the  constituents  of  the  fuel. 

Under  such  assumptions,  the  theoretical  elevation  in  tempera- 
ture, from  which  the  temperature  developed  by  the  combustion 
of  any  fuel  can  be  determined  may  be  expressed 

B.  t.  u.  produced  (21) 

W  x  c 

where  T= elevation  in  temperature, 

W— weight  of  products  of  combustion, 

<:— mean  specific  heat  of  products  between  temperature 
of  fuel  and  air  and  that  of  products. 

Since,  as  has  been  shown,  the  value  of  c  in  (21)  will  vary 
over  a  considerable  range  with  temperature,  this  expression  cannot 
be  used  for  a  direct  temperature  computation.  It  is  possible, 
however,  to  compute  the  theoretical  temperature  resulting  from 
the  combustion  of  a  given  fuel  under  given  conditions  by  the  use 
of  a  method  involving  trial  and  error  as  follows : 

Assuming  the  conditions  as  given  above,  the  heat  energy  of 
a  fuel  mixture  above  o  degrees  Fahrenheit,  plus  the  amount 
of  heat  generated,  must  equal  the  heat  energy  of  the  products  of 
combustion  above  o  degrees  Fahrenheit.  If  M  equals  the  sum 
of  the  fuel  constituents  (m l  +  m 2 + m3+  )  and  M l  the  sum  of  the 
constituents  of  the  products  of  combustion  ( 

35 


the  formula  for  the  determination  of  the  theoretical  temperature 
developed  may  be  expressed 

M^H-  Heat  generated*=M1^)  lta          (22) 

where  t^  =temperature  of  fuel  mixture, 

£2=temperature  evolved  in  combustion, 
Cp  and  £*,=mean  specific  heats  of  fuel  mixture  and  products 
of  combustion,  respectively. 

Since  /2  is  unknown,  c\  is  also  unknown,  and,  as  stated,  the 
method  of  trial  and  error  must  be  used.  This  method  is  best 
illustrated  by  example,  and  is  perhaps  most  fully  indicated  by  the 
consideration  of  a  gaseous  fuel.  Assume  then,  blast  furnace  gas 
having  an  analysis  as  follows : 


CO 


CH, 
CO, 


By  Volume 
Per  Cent 

27.36 
3.16 

•53 

IO.OO 

58.95 


By  Weight 
Per  Cent 

26.65 

•23 

•30 

15.40 

57.42 


If  this  gas  is  burned  with  20  per  cent  excess  air  the  products 
of  combustion  from  Table  8  will  be 


Weight 
per  Pound 
Gas 
Burned 

Theoretical  Amount 
Pounds 

Products  of  Combustion 
Pounds 

02 

Air 

C02 

N2 

H2O 

02 

CO 
H2 
CH4 
C02 

N2 

.2665 
.0023 
.0030 
.1540 
•5742 

•1519 
.0184 
.0120 

.6556 

•0795 
.0518 

.4184 

.0083 
.1540 

•5037 
.0611 
.0398 

.0207 
.0068 

,     .     . 

•5742 

20  per  cent  excess    .     .    . 

.7869 
•1574 

• 

.1210 

' 

.0364 

Total  Products 

.5807 

1.2998 

.0275 

.0364 

*It  is  to  be  noted  in  the  case  of  fuels  containing  hydrogenous  constituents,  since  no 
condensation  of  water  vapor  occurs,  the  lower  or  available  heat  value  of  such  constituents 
is  the  proper  value  for  use  in  the  computations.  These  values  may  be  taken  from  Table  6. 


If  the  temperature  of  the  fuel  mixture  before  combustion  is 
250  degrees  Fahrenheit,  the  computations  involved  in  the  use  of 
formula  (22)  under  the  assumed  conditions,  expressed  in  tabular 
form,  are : 


Composition 
of  Fuel 
Mixture 

M 

Lower 
Heat  Value 
H* 

JM,      1  I  7-' 

Mean 
Specific  Heat 

'   A-250 

CO 

.2665 

4380 

1167 

.2369 

.063134 

H2 

.0023 

52900 

122 

3.3665 

.007743 

CH4 

.0030 

21670 

65 

•5510 

.001653 

C02 

.1540 

.       .       . 

.2084 

.032094 

Oo 

.0764* 

2178 

OO7Q28 

.2369 

.164693 

.     .     . 

.      .      . 

1354 

.      .      . 

.277245 

*From  20  per  cent  excess  air. 


tincludes  N2  from  excess  air. 


The  heat  energy  of  the  fuel  mixture  above  o  degrees  will 
be  then 

.^=.277245x250=69.31  B.  t.  u. 


Since  t^  is  unknown  it  is  necessary  to  assume  a  trial  value  in 
order  to  compute  Cp^.  With  cpo_t^  computed  for  such  trial 
value,  formula  (22)  may  be  solved  for  t^  and  the  value  of  t^  so 
determined  used  for  a  second  trial. 

If  then  we  assume  /2,  the  theoretical  temperature  evolved 
under  the  conditions  of  combustion  given,  as  3000  degrees 
Fahrenheit,  we  have 


N 


Products— M' 

.5807 

.0364 

.0275 

1.2998 


#0-3000 
.2747 

•2439 

•5437 
.2658 


Substituting  in  formula  (22)  9 

69.31  +  1354^.528835 
^=2710  degrees 


.159518 

.008878 
.014952 
•345487 
•528835 


37 


Using  as  a  second  trial  value  /2=  2750  degrees,  we  have 

Products-M'  ^-2750  M'.  O>^7So 

CO3  .5807  .2715  .157660 

O2  .0364  .2415  .008790 

H20  .0275  .5297  -014567 

Na  1.2998  .2632  .342107 

.523124 
Substituting  again  in  formula  (22) 

69.31  +  1354=.  523124*5, 
/3=272i  degrees 

The  theoretical  temperature  evolved  under  the  assumed  con- 
ditions will  thus  be  approximately  2735  degrees  Fahrenheit. 
The  above  method  may  be  continued  if  more  accurate  results 
are  desired. 

In  the  consideration  of  the  theoretical  temperature  it  is 
evident  that  the  time  element,  i.  e.t  the  length  of  time  necessary 
to  complete  combustion,  does  not  enter,  though  in  actual  practise 
this  is  an  appreciable  factor. 

In  practise,  the  temperature  which,  for  a  given  fuel,  is  theo- 
retically possible,  is  never  obtained.  The  main  factor  in  the 
burning  of  ordinary  fuels  which  results  in  a  temperature  below 
that  theoretically  possible,  is  the  dilution  of  the  products  of 
combustion  through  the  introduction  of  a  greater  amount  of  air 
than  is  required  for  complete  oxidization,  i.  e.,  the  presence  of 
excess  air.  Under  such  conditions  there  are  present  in  the 
products  of  combustion  amounts  of  oxygen  and  nitrogen  in 
excess  of  the  amounts  required  for  combustion,  which  excess 
weights  must  be  heated  from  the  temperature  at  which  they  are 
introduced  to  the  ultimate  temperature  of  the  gases.  In  using  a 
portion  of  the  definite  amount  of  heat  that  a  given  fuel  will 
generate  for  so  increasing  the  temperature  of  these  excess  weights 
of  oxygen  and  nitrogen,  the  temperature  of  the  ultimate  mixture 
will  be  reduced  to  below  that  which  would  exist  were  there  no 
excess  gases  to  be  heated. 

Temperatures  below  the  theoretical  will  also  result  from  an 
insufficient  air  supply.  Under  such  conditions  there  is  a  loss  in 
the  heat  generated  due  to  incomplete  combustion  of  carbon 
(burning  to  CO  instead  of  CO2). 

38 


A  further  reduction  below  the  theoretical  temperature  occurs 
through  loss  in  radiation.  While  the  time  element  does  not  enter 
into  any  computation  involving  formula  (22),  in  practise,  since  the 
quantity  of  heat  radiated  from  a  given  mass  of  fuel  is  a  function 
of  the  time  during  which  combustion  takes  place,  it  is  obvious  that 
a  portion  of  the  heat  generated  will  be  lost  through  radiation, 
such  loss  increasing  as  combustion  is  slower. 

The  two  important  reactions  of  combustion 

2H0  and 


are  reversible  and  if  such  dissociation  occurs  it  would  have  a 
decided  effect  on  the  temperature  developed  in  combustion.  The 
amount  of  dissociation  which  takes  place  under  the  temperatures 
developed  in  boiler  furnace  practise  is  not  definitely  known  but 
is  probably  inappreciable.  For  usual  combustion  this  factor  may 
be  considered  as  negligible. 

From  the  factors  involved  it  is  evident  that  the  better  the  com- 
bustion, i.  e.,  the  more  complete  with  the  minimum  of  excess  air,  the 
higher  the  temperature  developed,  and  it  follows  that  the  better 
the  combustion  and  the  higher  the  temperature,  again  assuming 
the  ability  of  the  boiler  to  efficiently  absorb  heat,  the  better  the 
efficiency.  It  is  very  difficult  with  the  means  available  to  deter- 
mine accurately  the  actual  temperature  developed  in  furnace 
combustion,  and  hence  to  make  use  of  such  temperature  as  a 
measure  of  the  efficiency  of  combustion.  Fortunately  there  are 
other  methods  by  which  such  efficiency  may  be  determined  with 
a  considerable  degree  of  accuracy. 

FLAME 

The  appearance  of  combustion,  i.  e.t  the  "look"  of  the  mass  of 
fuel  and  of  the  products  of  combustion,  offers  to  the  experienced 
eye  a  measure  of  the  temperatures  developed.  While  the  use 
of  such  a  method  can  lead  only  to  the  most  approximate  results, 
and  at  best  serve  simply  as  a  check  of  more  accurate  determi- 
nations, it  is  perhaps  worth  while  to  consider  it. 

The  physical  evidence  by  which  the  temperature  and  the 
degree  and  the  extent  of  combustion  in  a  boiler  furnace  may 
be  judged,  is  the  appearance  of  the  flame,  the  fuel  itself  being 
visible  but  rarely.  Flame  may  be  denned  as  a  mass  of  intensely 

39 


heated  gas  in  a  state  of  combustion,  though  it  is  possible  for 
flame  to  exist  as  gas  not  actually  in  such  state.  The  luminosity 
of  flame,  or  the  characteristic  which  gives  its  visibility,  is  due  to 
the  heating  to  incandescence  of  the  unconsumed  particles  of 
combustible  matter  present  in  the  gases,  and  the  variation  in  the 
colors  of  flame  is  due  to  the  difference  in  the  degree  of  heat  com- 
municated to  these  particles.  The  higher  the  temperature  of 
these  particles  the  whiter  the  flame.  The  length  and  volume 
of  the  flame  will  vary  with  the  combustible  elements  present, 
and  the  thoroughness  with  which  the  air  and  combustible  ele- 
ments are  mingled,  and  since  such  number  will  decrease  with  an 
increase  in  the  completeness  of  combustion,  the  shorter  the  flame, 
in  the  absence  of  any  outside  cooling  medium,  the  more  rapid  and 
complete  the  combustion. 

If  it  were  possible  for  the  combustion  of  any  fuel  to  be  com- 
plete and  instantaneous  there  would  be  no  visible  flame,  since 
both  carbon  dioxide  and  water  vapor  are  invisible.  Visible  flame, 
then,  is  evidence  of  incomplete  or  non-combustion,  but  such 
evidence  in  the  boiler  furnace  means  simply  that  the  com- 
bustion has  not  taken  place  with  sufficient  rapidity  to  evolve  heat 
instantaneously. 

It  follows  from  the  above  that  for  a  given  amount  of  fuel 
burned,  a  short  flame  will  ordinarily  mean  rapid  and  complete 
combustion,  a  longer  flame  delayed  combustion,  and  a  very  long 
flame  imperfect  or  non-combustion. 

TABLE  7A 
TEMPERATURE  AND  APPEARANCE  OF  FLAME* 


(Appearance  of  Flame 

Temperature 
Degrees  Fahrenheit 

Dark  Red      

Q7  S 

Dull  Red  

I2QO 

Dull  Cherry  Red    

I4.7O 

Full  Cherry  Red     

1  6  HO 

Clear  Cherry  Red            

iS^O 

Deep  Orange          . 

2OIO 

White  

217O 

Bright  White     

2^0 

Dazzling  White      , 

27  7O 

*Jos.  W.  Hays. 


40 


The  temperature  evolved  in  combustion  may  be  approximated 
from  the  appearance  of  the  fuel  mass  or  the  flame  in  accordance 
with  the  preceding  table.  Such  figures  are  of  necessity  but  the 
roughest  approximations,  but,  in  connection  with  the  flame  length, 
are  of  some  value  where  apparatus  for  more  accurate  determina- 
tion of  the  extent  and  degree  of  combustion  is  not  available. 


AIR  AND  COMBUSTION 

THUS  far,  in  the  abstract  consideration  of  combustion, 
the  presence  of  sufficient  oxygen  for  combination  with 
oxidizable  substances,  and  of  a  temperature  sufficient  to 
bring  about  the  chemical  combinations  of  combustion,  have 
simply  been  assumed.  As  a  matter  of  fact,  given  proper  tem- 
perature conditions,  it  is  the  physical  introduction  of  oxygen  into 
the  presence  of  combustible  substances  in  such  manner  as  to 
assure  complete  oxidization,  and  at  the  same  time  to  assure  the 
utilization  of  all  or  of  the  maximum  proportion  so  supplied, 
that  is  the  most  important  and  difficult  problem  in  the  burning 
of  all  fuels. 

The  source  of  supply  of  the  oxygen  necessary  for  combustion 
is,  as  stated,  the  air.  From  the  proportionate  parts  by  weight 
of  oxygen  and  nitrogen  as  given,  namely,  O  2  —  23.15  per  cent 
and  N 3  —  76.85  per  cent,  it  is  obvious  that  to  supply  one  pound 
of  oxygen  for  combustion  it  will  be  necessary  to  supply 

1-^.2315^4.320 

pounds  of  air,  and  that  in  this  weight  of  air  there  will  be 
3.32  pounds  of  nitrogen  which  serves  no  useful  function  in 
combustion. 

We  have  seen  in  Table  2,  the  chemical  combinations  occurring 
in  the  union  of  oxygen  with  the  combustible  elements  and  com- 
pounds found  in  the  fuels  ordinarily  used  for  the  generation  of 
heat.  From  the  manner  of  such  combinations  and  dissociations, 
and  a  consideration  of  the  atomic  weights  of  the  elements  in- 
volved, the  proportionate  part  by  weight  of  the  elements  entering 
into  the  resulting  compounds  may  be  readily  computed  as  well  as 
the  weights  of  the  products  of  combustion.  With  the  amount  of 
oxygen  required  for  combustion  thus  known  the  amount  of  air 
required  will  be  indicated  from  the  oxygen — nitrogen  ratio  exist- 
ing in  air. 

The  methods  of  such  computations  are  clearly  indicated  by 
example,  and  since  the  relation  of  the  products  of  combustion 
to  the  combustible  elements  of  the  fuel  is  the  most  important 
factor  in  the  determination  of  the  efficiency  of  combustion,  it 
appears  advisable  to  illustrate  such  computations  fully. 

42 


Consider  first  carbon : 

From  Table  2  it  was  seen  that  one  atom  of  carbon  united 
with  two  atoms  of  oxygen  to  form  carbon  dioxide 

C  +  20=C02 

From  the  atomic  weights 

i2+(2xi6)=44 

or  in  the  burning  of  one  pound  of  carbon  to  carbon  dioxide, 
twelve  parts  by  weight  of  carbon  combine  with  thirty-two  parts 
by  weight  of  oxygen  to  form  forty-four  parts  by  weight  of 
carbon  dioxide.  Hence,  any  weight  of  carbon  dioxide  must  be 
composed  of  27.27  per  cent  by  weight  of  carbon  and  72.73 
per  cent  by  weight  of  oxygen,  or 

i  pound  CO2  =  .2727  pounds  €  +  .7273  pounds  O2 

Since  the  ratio  of  carbon  to  oxygen  in  carbon  dioxide  is 
i  to  2.667,  it  is  obvious  that  in  burning  one  pound  of  carbon  to 
carbon  dioxide,  2.667  pounds  of  oxygen  will  be  required. 

If  one  pound  of  oxygen  is  contained  in  4.32  pounds  of  air  it 
will  be  necessary  to  supply  for  the  complete  combustion  of  one 
pound  of  carbon 

2.667x4.32=11.52 

pounds  of  air,  and  since  each  pound  of  oxygen  is  accompanied  by 
3.32  pounds  of  nitrogen,  there  will  pass  off  with  the  carbon  dioxide 

2.667x3.32=8.85 
pounds  of  nitrogen. 

In  the  complete  combustion  of  one  pound  of  carbon  then  the 
resulting  products  of  combustion  will  be 

i  pound  C  +  2.667  pounds  O2  =  3-667  pounds  CO2 
2.667x  3.32  pounds  N2  =8.885  pounds  N2 

Again,  consider  hydrogen: 

Table  2  indicates  that  two  atoms  of  hydrogen  will  combine 
with  one  atom  of  oxygen  to  form  water  vapor 

2H4-0=H20 
From  the  atomic  weights 

(2x  1)4-16=18 

or  in  the  burning  of  one  pound  of  hydrogen  to  water  vapor,  one 
part  by  weight  of  hydrogen  will  combine  with  eight  parts  by 

43 


weight  of  oxygen  to  form  eighteen  parts  by  weight  of  water  vapor. 
Hence,  in  one  pound  of  water  vapor  we  have 

I  pound  H2O  —  .in  pounds  H2+.889  pounds  O2 

Since  the  ratio  of  hydrogen  to  oxygen  in  water  vapor  is  thus 
i  to  8  it  will  require  8  pounds  of  oxygen  for  the  complete  com- 
bustion of  one  pound  of  hydrogen,  which  means,  as  for  the 
combustion  of  carbon, 

8x4.32—34.56 

pounds  of  air  required  to  burn  one  pound  of  hydrogen. 
The  nitrogen  present  in  this  weight  of  air  will  be 

8  x  3.32=26.56  pounds  N2 
and  the  products  of  combustion  of  one  pound  of  hydrogen  will  be 

i  pound  H2  +  8  pounds  Oa=9  pounds  H2O 
8  x  3.32  =26.56  pounds  N2 

As  typical  of  the  combustible  compounds  consider  ethylene 
(the  CH  series  are  all  computed  in  a  similar  manner) 

C2H4=2C  +  4H 

or  from  atomic  weights 

28=24  +  4 

Thus  one  pound  of  ethylene  is  composed  of 

.857  pounds  €+.143  pounds  H 
To  burn  .857  pounds  of  carbon  will  require 

.857  x  2.667=2.2856  pounds  O2 
To  burn  .143  pounds  of  hydrogen  will  require 

.143  x  8=1.144  pounds  O2 
The  total  oxygen  required  then  will  be 

2.286+  1.144=3.430  pounds 
and  the  total  air 

3.43  x  4.32  =  14.82  pounds 


The  products  of  combustion  will  be 


coa        HSO        N, 

Pounds   Pounds   Pounds 


.857  pounds  C  +  2.286  pounds  O2  =3.143     ...... 

.143  pounds  H2+  1.144  pounds  O2          =.  .  .     1.287    .  .  . 
14.82  pounds  air  x  .7685  (per  cent  N  in  air)  =  ......    H-39 


44 


The  methods  of  computation  are  simple  but,  as  stated,  are 
considered  at  length  because  oi  their  importance,  particularly  in 
the  case  of  gaseous  fuels.  Table  8  gives  the  results  of  such 
computations,  in  terms  of  weight,  for  all  of  the  combustible 
elements  and  compounds  encountered  in  the  usual  fuels. 
Table  9  gives  such  values  in  terms  of  volume. 

TABLE  8 
COMBUSTION    DATA 

IN  TERMS  OF  POUNDS  PER  POUND  OF  FUEL 


Mole- 
cular 
Symbol 

Theoretically 
Required 
Pounds 

Products  of  Combustion 
Pounds 

02 

Air 

CO, 

H,O 

N, 

CO 

S02 

Carbon  (to  CO  2  )    . 
Carbon  (to  CO)      . 
Carbon  Monoxide  . 
Sulphur     .... 
Hydrogen  .... 
Methane    .... 
Acetylene  .... 
Ethylene    .... 
Ethane.     .     .     .     . 
Hydrogen  Sulphide 

c 
c 

CO 

s 

H2 
CH4 
C2H2 
C2H4 
C2H6 
H2S 

2.667 

1-333 
0.572 
I.OOO 

8.000 
4.000 
3-°77 
3429 
3733 
1.412 

H.52 
5.76 
2.46 

4-32 
34-56 
17.28 
13.29 
14.81 
16.13 

6.10 

3.667 

1-57 

2-75 
3-39 
3-i4 
2-93 

.     .     . 

8.85 

4-43 
i.  80 

2-333 

.   .   . 

9.00 
2.25 
0.69 
1.29 
1.80 
o-S3 

3-32 
26.56 
13.28 

IO.2I 
11.38 
I2.4O 
4.69 

.    .    . 

2.00 

.    .     . 

.   .   . 

.    .    . 

1.88 

TABLE  9 
COMBUSTION  DATA 

IN  TERMS  OF  CUBIC  FEET  PER  CUBIC  FOOT  OF  FUEL 


Mole- 
cular 
Symbol 

Theoretically 
Required 
Cubic  Feet 

Products  of  Combustion 
Cubic  Feet 

0, 

Air 

CO, 

HaO 

N, 

CO 

SO, 

Carbon  Monoxide  . 
Hydrogen  .... 
Methane    .... 
Acetylene  .... 
Ethylene    .... 
Ethane       .... 
Hydrogen  Sulphide 

CO 
H2 
CH4 
C2H2 
C2H4 
C2H6 
H2S 

o-5 
o-5 

2.0 
2-5 

3-o 
3-5 
i-5 

2.391 
2.391 
9-564 

"•955 
14.346 

16.737 
7.173 

I 

I 

2 
2 
2 

2 

I 
2 

3 

i 

1.891 
1.891 
7.564 

9-455 
11.346 

I3-237 
5-673 

.  .   . 

.   .   . 

.    ....      . 

I 

Considered  from  a  chemical  standpoint,  the  supplying  of  just 
the  proper  amount  of  oxygen  or  of  air  for  perfect  combustion,  as 


indicated  by  Table  8,  appears  simple.  It  is,  however,  the  physical 
difficulty  encountered  in  the  introduction  of  just  the  proper 
amount  of  oxygen  that  is  the  main  source  of  the  losses  occurring 
in  the  burning  of  any  fuel. 

It  may  be  well  to  distinguish  here  between  perfect  and  com- 
plete combustion.  Perfect  combustion,  as  shown  in  Table  8,  is 
the  result  of  supplying  the  requisite  amount  of  oxygen  for 
union  with  all  of  the  oxidizable  constituents  of  the  fuel  and 
utilizing  in  combustion  all  of  the  oxygen  so  supplied.  Complete 
combustion  on  the  other  hand,  results  from  the  oxidization  of 
all  the  combustible  constituents  of  the  fuel  but  does  not  of 
necessity  imply  the  utilization  of  all  of  the  oxygen  supplied. 
If  perfect  combustion  could  be  accomplished  in  a  boiler  furnace 
there  would  be  no  unavoidable  combustion  losses.  While  com- 
bustion is  complete  but  not  perfect,  there  are,  as  will  be  shown, 
losses  due  to  the  supplying  of  too  great  an  amount  of  oxygen, 
and  hence  air,  and  it  follows  that  the  more  nearly  complete 
combustion  can  be  made  to  approach  perfect  combustion,  the  less 
the  loss  that  will  occur  in  the  burning  of  any  fuel.  It  is  in  fact 
this  problem — the  seeking  after  perfect  combustion — that  is  the 
problem  of  furnace  design. 

It  is  obvious  from  the  foregoing  that  the  real  measure  of  the 
efficiency  of  combustion  is  to  be  found  in  the  relations  existing 
between  the  amount  of  air  theoretically  required  for  the  burning 
of  any  fuel  and  the  amount  of  air  actually  supplied  for  such 
combustion  and  before  considering  the  possible  furnace  losses 
resulting  either  from  incomplete  combustion  or  from  the 
supplying  of  too  great  an  amount  of  oxygen  it  is  necessary  to 
understand  the  method  of  determining  these  relations. 

The  calculations  involved  in  the  determination  of  the  weight 
of  air  required  for  the  perfect  combustion  of  a  pound  of  a  given 
fuel  have  been  indicated  in  the  computations  of  Table  8.  For 
such  determination  an  analysis  of  the  fuel  is  necessary,  this 
analysis  in  the  case  of  solid  and  liquid  fuels  being  given  in  terms 
of  weight,  and  in  the  case  of  gaseous  fuels  either  in  terms  of 
weight  or  of  volume.  While  the  analysis  of  gaseous  fuels  is 
ordinarily  given  in  terms  of  volume,  it  is  perhaps  best  to  trans- 
form such  analysis  to  a  weight  basis,  since  the  results  are  usually 
desired  in  terms  of  weight. 

46 


With  the  data  of  Table  8  available,  the  development  of 
formulae  to  give  directly  the  theoretical  amount  of  air  necessary 
for  the  perfect  combustion  of  any  fuel  is  simple.  Such  formulae 
are  given  hereafter.  There  are,  however,  no  suitable  or  reliable 
means  of  measuring  or  weighing  the  air  actually  admitted  to  a 
boiler  furnace,  and  the  only  means  of  determining  the  amount 
of  such  air  is  from  the  analysis  of  the  products  of  combustion — 
ordinarily  called  flue  gases.  In  making  use  of  such  analysis 
certain  assumptions,  discussed  hereafter,  are  necessary,  but 
these  assumptions  are  such  that  the  results  obtained  from  the 
proper  consideration  of  a  properly  made  analysis  are  well  within 
the  error  of  a  boiler  test  as  a  whole. 

The  apparatus  used  in  the  determination  of  the  constituents 
of  flue  gases  and  the  methods  of  operating  such  apparatus  have 
been  too  often  described  to  need  discussion  here.  In  the  ordi- 
nary routine  analysis  the  proportionate  parts  by  volume  of 
carbon  dioxide,  carbon  monoxide  and  oxygen  are  determined, 
the  difference  between  the  sum  of  these  constituents  and  100 
per  cent  being  assumed  as  nitrogen. 

Where  combustion  is  complete,  regardless  of  the  amount  of 
excess  air,  the  only  products  of  combustion  that  can  result  from 
the  burning  of  any  fuel  are  CO2,  SO2  (or  SO3),  H2O  and  N§. 
The  ordinary  routine  analysis  then  is  in  reality  simply  a 
measure  of  the  completeness  of  combustion  of  the  carbon  content 
of  a  fuel.  Properly  used,  however,  such  analysis  may  be  made 
to  give  combustion  data  from  which  furnace  losses  may  be  com- 
puted within  the  required  limits  of  accuracy. 

It  seems  proper  to  emphasize  here  the  necessity,  where 
accurate  results  are  desired,  of  considering  flue  gas  analyses  only 
in  conjunction  with  analyses  of  the  fuel  burned.  As  an  example 
of  the  errors  that  may  arise  where  the  two  analyses  are  not 
considered  together  we  may  take  the  tables  of  preventable  losses 
corresponding  to  varying  percentages  of  carbon  dioxide  present 
in  the  flue  gases,  which  are  given  in  numerous  publications. 
Such  tables  give  an  arbitrary  percentage  of  carbon  dioxide  which, 
if  it  could  be  obtained,  would  represent  no  preventable  furnace  loss, 
with  increasing  losses  for  lesser  percentages  of  carbon  dioxide. 

For  any  fuel  there  will  be  a  definite  percentage  of  carbon 
dioxide  that  must  correspond  to  perfect  combustion  and  hence 

47 


to  zero  preventable  loss,  but  such  percentage  will  vary  not  only 
for  different  classes  of  fuels  but  even  widely  with  different  fuels 
of  the  same  class.  How  wide  this  variation  in  carbon  dioxide 
may  be  for  perfect  combustion  with  different  fuels  is  indicated 
by  the  computations  of  combustion  data  given  later,  the  range 
in  the  examples  of  fuel  taken  being  from  9.4  per  cent  in  the 
case  of  by-product  coke  oven  gas  to  25.1  per  cent  in  the  case  of 
blast  furnace  gas.  From  these  figures  it  is  obvious  that  CO2 
tables  are  not  to  be  accepted  as  a  measure  of  preventable  furnace 
loss,  regardless  of  the  class  of  fuel  burned,  and  that  for  the 
intelligent  use  of  a  flue  gas  analysis,  an  analysis  of  the  fuel 
burned  is  also  essential. 


48 


COMBUSTION  FORMULAE 
AIR  REQUIRED  FOR  COMBUSTION 

WITH  carbon,  hydrogen,  and  sulphur  the  only  com- 
bustible   elements    found    in    the    fuels    used    for 
commercial  steam  generation,  it  is,  as  stated,  a  simple 
matter  from  the  data  of  Table  8,  to  construct  a  formula  for  the 
amount  of  air  theoretically  required  for  the  complete  combustion 
of  a  pound  of  any  fuel.     This  may  be  expressed  as  follows: 

Pounds  air  required  per  pound  fuel= 
11.52  C+34-56  (H—  -)  +  4.32  S  (23) 

where  C,  H,  O  and  S  represent  the  percentages  by  weight  of 
carbon,  hydrogen,  oxygen  and  sulphur.*  As  in  the  case  of  for- 

mula (^),  the  term    (H  —  —  )    assumes   that  all  of  the  oxygen 

constituent  is  free  to  unite  with  the  hydrogen  to  form  water 
vapor,  such  an  assumption  in  the  computation  of  the  amount  of 
air  required  leading  to  a  negligible  error.  This  formula,  reduced 
to  the  simpler  form  in  which  it  is  ordinarily  used  becomes 

Pounds  air  required  per  pound  fuel= 

34.56  (y+[H—  J]+f)  04 

In  the  case  of  gaseous  fuels,  it  would  be  necessary,  in  order 
to  make  use  of  formula  (24.),  to  break  the  hydro-carbons  into 
their  constituent  elements,  and  it  is  simpler  to  make  use  of  a 
formula  based  directly  upon  the  data  of  Table  8.  For  this  class 
of  fuels  the  formula  may  be  expressed  as  follows: 

Pounds  air  required  per  pound  fuel= 

246  CO+34-56  H2+i7.28CH4+i3.29C2H2+i4.8iC2H4  + 
16.13  C2H6  +  6.io  H2S—  4-32  O2 


With  gaseous  fuels,  where  the  analysis  is  commonly  given  on 
a  volumetric  basis,  it  is  sometimes  desirable  to  express  the  amount 


*While  the  constants  are  those  determined  in  the  calculations  for  Table  8. 

49 


of  air  required  in  terms  of  cubic  feet.    On  the  basis  of  the  data  of 
Table  9,  formula  (-25),  becomes  then 

Cubic  feet  air  required  per  cubic  foot  gas— 

2.39(CO+H9)+9.56  CH4  +  1  1.98  C2H2+  14.35  C2H4  + 
1674  C2H6—  4.78  02  (*6) 

PRODUCTS  OF  COMBUSTION 

The  data  of  Table  8  also  make  it  possible  to  determine 
directly  what  the  products  of  theoretically  perfect  combustion 
will  be. 

Products  of  combustion  per  pound  of  fuel: 


S  02=2.  S 

. 

N2=8.85  C+26.56  H2-f  3.32  S+N2 

With  the  actual  weights  of  the  products  of  combustion  thus 
known,  they  may  be  expressed  in  terms  of  percentage  by  weight, 
and  if  desired  these  latter  values  may  readily  be  transformed  into 
values  giving  percentages  by  volume. 

As  in  the  case  of  air  required  for  combustion  it.  is  perhaps 
simpler  to  express  the  products  of  combustion  of  a  gaseous  fuel 
directly  in  terms  of  the  data  of  Table  8. 

Products  of  combustion,  one  pound  fuel  = 

C03  =  i.57   CO  +  2.75   CH4  +  3.39   C2H2  +  3.i4  C2H4  + 
2.93C2H6  +  C02 

H20=9(H—  j)  +  2.25  CH4  +  o.69  C2H2  +  i.29  C2H4  + 
i.8oC2H6  +  o.53H2S  +  H20 

SO2=i.88H2S 

N,  =  i.89  €0+26.56  Ha+  13.28  CH4+  10.21  C2H2  + 
12.38  C2H4  +  i2.40  C,He  +  4.69  H3S+N2 

5° 


Expressed  in  volumetric  terms  : 

Products  of  combustion,  one  cubic  foot  fuel  = 


H20=H-f  2  CH4  +  C2H2  +  2  C2H4  +  3  C2H6  + 
S02=H2S 

N2  =  i.89    CO  +1.89    H2  +  7-56    CH4  +  9.45    C2H2  + 
11.35  C2H4  +  13.24  C2H6+5.67  H2S+N2 

COMBUSTION  DATA  FROM  GAS  ANALYSIS 
A  flue  gas  analysis  may  be  used,  as  will  be  shown,  in  con- 
junction with  the  analysis  which  would  result  from  the  perfect 
combustion  of  a  fuel,  to  give  the  necessary  data  for  a  computation 
of  combustion  losses.  Its  generally  accepted  use,  however,  is 
its  application  in  a  formula  which  is  assumed  to  give  directly 
the  weight  of  dry  gas  per  pound  of  carbon  or  of  fuel  burned, 
which  weight  is  that  used  in  combustion  loss  calculations.  This 
formula  is 

Pounds  dry  gas  per  pound  carbon  = 


ii    C02  +  8    02+;  2 

3    (C02-hCO) 

where  the  symbols  represent  the  proportionate  parts  by  volume 
of  the  constituents  of  the  gas  analyzed. 

Properly  used,  this  formula  gives  results  which  are  accurate 
well  within  the  limits  of  error  of  boiler  testing.  Unfortunately, 
however,  the  formula  is  too  frequently  presented  without  ex- 
planation of  its  derivation,  or  without  discussion  of  the  assumption 
upon  which  it  is  based,  and  for  intelligent  use,  it  would  appear 
that  both  of  these  factors  should  be  considered. 

The  only  gases  which  can  exist  in  the  products  resulting 
from  the  combustion  of  carbon  are  carbon  dioxide,  carbon  mon- 
oxide, oxygen  and  nitrogen,  all  of  the  carbon  coming  from  the 
fuel  while  the  oxygen  and  nitrogen  are  from  the  air  introduced 
for  combustion. 

If  we  assume  that  all  of  the  dry  gas  resulting  from  the  com- 
bustion of  any  fuel  is  due  to  the  oxidization  of  carbon,  either  free 
or  combined,  which  assumption  would  be  correct  if  we  neglect 
the  sulphur  constituent  of  the  fuel,  the  weight  of  carbon  burned 


in  the  fuel  times  the  weight  of  dry  products  of  combustion  per 
pound  of  carbon  must  equal  the  total  weight  of  dry  products. 
This,  expressed  as  a  formula,  is,  in  terms  of  weights  per  pound 
of  fuel, 

Weight  of  C  burned  x  dry  gas  per  pound  C=total  dry  gas 
or 

Total  dry  gas  per  pound  fuel 

Dry  gas  per  pound  C=.ir  .  «     ^  ;,  — n= — ,   («) 

Weight  C  burned  per  pound  fuel 

The  actual  weight  of  carbon  in  the  fuel  must  reappear  in  the 
flue  gases  in  the  same  amount  either  as  carbon  dioxide  or  carbon 
monoxide  and  (a)  may  be  written  as 

Total  dry  products 

Dry  gas  per  pound  C— ,ir  .  ,  ^  ^  . — 5 (<*) 

Weight  C  in  flue  gases 

This  relation  must  hold  whether  expressed  in  terms  of  actual 
weights  or  in  terms  of  percentage  by  weights  and  (b)  thus  may 
be  written 

100 
Dry  gas  per  pound  <  A  CQ3+  »  CO 

••         „  PC...  c-  ' 

where  the  symbols  represent  percentages  by  weight. 

Formula  (c)  may  be  transferred  to  volumetric  form  by  multi- 
plying each  term  by  its  relative  density  (see  page  19)  and  becomes 

ii  CCL+8  CL+7  (CO  +  N.) 
Dry  gas  per  pound  C—  3  (COa  +  CO) 

the  symbols  representing  the  volumetric  percentages  of  the  con- 
stituent gases  as  given  by  a  flue  gas  analysis. 

The  principal  assumption  of  formula  (27)  is  that  the  analysis 
as  used  is  of  dry  gas. 

All  fuels  in  common  use  contain  a  greater  or  lesser  amount 
of  moisture.  The  loss  due  to  such  moisture  is  computed  where 
a  heat  balance  is  given  but  the  weight  of  this  moisture  is  some- 
times overlooked  in  computing  total  gas  weight.  All  air  supplied 
for  combustion  also  contains  a  certain  amount  of  moisture,  and 
though  this  weight  may  be  computed  and  the  loss  resulting 
therefrom  determined,  the  weight  is  ordinarily  inappreciable 
and  the  loss  commonly  included  with  the  unaccounted  losses. 

52 


Aside  from  the  moisture  in  the  fuel  and  in  the  air  supplied 
for  combustion,  which  moisture  will  appear  as  water  vapor  in  the 
flue  gases,  there  will  also  be  an  appreciable  weight  of  water  vapor 
due  to  the  burning  of  the  hydrogen  content  of  the  fuel.  This 
weight,  with  perfect  combustion,  may  be  as  high  as  1 5  per  cent 
of  the  total  for  certain  gaseous  fuels.  (See  by-product  coke 
oven  gas,  page  95.) 

We  have  then  present  in  the  flue  gases,  but  not  measured  in 
the  ordinary  analysis,  a  considerable  amount  of  moisture  in  the 
form  of  water  vapor.  Water  is  commonly  used  as  the  displace- 
ment medium  in  the  collection  of  the  sample  of  gas  for  analysis, 
and,  further,  during  the  analysis  itself  the  gas  sample  comes  into 
contact  with  water.  The  effect  of  these  various  factors  tends 
toward  a  saturation  of  the  gas  being  analyzed  and  from  the 
results  obtained  with  all  classes  of  fuel  the  assumption  seems 
warranted  that  such  gases  are  actually  saturated.  Under  these 
conditions  proportionate  parts  of  the  water  vapor  content  of 
the  gas  will  be  absorbed  with  the  different  constituents  of  such 
gas  and  the  resulting  analysis  may  be  safely  assumed  to  be 
that  of  a  dry  gas.  How  nearly  correct  such  an  assumption  is 
may  be  seen  from  the  various  examples  of  the  computations  of 
combustion  data  which  follow. 

A  further  source  of  error  in  formula  (.27)  is  one  resulting 
from  the  presence  of  sulphur  in  numerous  fuels.  Such  sulphur, 
as  shown  in  Table  2,  ordinarily  burns  to  SO2,  which  will  be 
absorbed  in  the  flue  gas  analysis  as  carbon  dioxide.  With  fuels 
low  in  sulphur  the  error  arising  from  this  source  is  small  and  can 
be  safely  neglected.  With  fuels  high  in  sulphur  and  low  in 
carbon,  however,  as  in  the  case  of  certain  middle  western  coals, 
the  error  may  be  of  sufficient  amount  to  warrant  consideration. 
In  an  example  given  later  for  a  coal  containing  4.42  S  and 
61.25  per  cent  C.  the  error  is  shown  to  be  as  great  as  4 
per  cent. 

It  is  entirely  possible  in  determining  the  weight  of  dry 
products  of  combustion  per  pound  of  fuel  from  formula  (27)  to 
modify  the  actual  carbon  weight  as  given  by  the  ultimate  analysis 
to  correct  for  the  sulphur  content  of  the  fuel,  and  where  accuracy 
is  desired,  and  the  sulphur  content  is  appreciable,  such  a  cor- 
rection should  be  made. 


53 


The  first  term  of  formula  (27),  viz.  (i  i  CO3-:~[3(CO2-f  CO)]) 
represents  not  only  the  weight  of  CO2  resulting  from  the  com- 
bustion of  carbon,  but  includes  as  well  the  SO2  resulting  from 
the  combination  of  sulphur.  If  the  weight  of  CO 2  and  SO2  result- 
ing from  the  combustion  of  one  pound  of  carbon  and  one  pound 
of  sulphur,  respectively,  were  the  same,  the  necessary  correction, 
for  the  proper  determination  of  the  weight  of  dry  products  of 
combustion  per  pound  of  fuel  from  formula  (27)  could  be  made 
by  adding  the  sulphur  content  to  the  carbon  content  of  the 
fuel.  The  CO2  resulting  from  the  combustion  of  one  pound  of 
carbon,  however,  is,  from  Table  8,  3.667  pounds,  while  the  weight 
of  SO 2  from  one  pound  of  sulphur  is  2.00  pounds.  The  corrective 
factor  must  be  in  the  ratio  of  these  weights,  and  the  correct  value 

instead  of  being  (C+  S)  will  be  (C  +  ^ — ).     The  weight  of  dry 
products  of  combustion  per  pound  of  fuel  then  instead  of  being 


xC  (27-0) 


ii  co3+soa+7(n3+co) 

3(C02+CO) 

should  be,  where  accuracy  is  desired, 

iiCOa+802+7(N2+CO) 
3  (C03+C0) 

Formula  (27)  then,  may  be  accepted  as  correct  for  any 
fuel,  for  the  computation  of  the  data  which  it  is  presumed 
to  give,  namely,  the  weight  of  dry  gas  per  pound  of  carbon, 
or  by  multiplying  the  weight  so  determined  by  the  weight  of 
carbon  in  the  fuel  properly  corrected  for  the  sulphur  equivalent, 
the  weight  of  dry  gas  per  pound  of  fuel.  It  is  not  to  be  accepted 
however,  without  additional  data  in  the  way  of  fuel  analysis,  in 
the  computation  of  total  gas  weights  or  in  the  computation  of  the 
amount  of  air  supplied  for  combustion.  The  chief  reason  for  this 
statement  lies  in  the  fact  that  practically  all  fuels  contain  a 
certain  amount  of  hydrogen.  The  oxygen  supplied  for  the  com- 
bustion of  this  hydrogen  does  not  appear  in  the  dry  flue  gases 
and  is  not  accounted  for  by  formula  (27),  while  the  nitrogen 
which  accompanied  the  oxygen  so  utilized  does  appear  in  the  dry 
gases  and  in  the  analysis.  It  is  not  always  made  clear  why,  in 
spite  of  this  fact,  formula  (27)  can  be  safely  used  for  the  com- 
putation of  the  dry  gas  per  pound  of  carbon  or  per  pound  of 

54 


fuel,  and  a  word  of  explanation  on  this  feature  seems  advisable. 
The  carbon  content  of  the  fuel  must  all  appear  in  the  dry  gases 
in  the  exact  amount  *  as  in  the  fuel,  either  as  carbon  dioxide 
or  as  carbon  monoxide.  The  basis  of  formula  (27)  is,  as  has  been 
shown,  simply  the  weight  relation  between  a  known  quantity  of 
one  constituent  of  the  dry  gases  (carbon)  and  the  total  weight  of 
such  gases,  regardless  of  the  composition  of  such  total  weight 
or  the  sources  of  its  constituents,  and  with  the  weight  and  the 
percentage  weight  of  a  single  constituent  known,  the  total  weight 
is  obvious. 

AIR  SUPPLIED  FOR  COMBUSTION 

A  number  of  formulae  based  upon  a  volumetric  flue  gas 
analysis  have  been  offered  for  the  computation  of  the  weight  of 
air  supplied  per  pound  of  fuel  burned.  While  certain  of  these 
formulae  give  reasonably  accurate  results  for  specific  classes  of 
fuels,  none  is  applicable  to  all  fuels. 

Unquestionably  the  best  method  of  determining  the  weight 
of  air  supplied,  and  in  fact  the  only  method  that  may  be  safely 
used  for  all  fuels,  is  through  the  use  of  formula  (27)  or  (27-$) 
giving  the  dry  products  of  combustion  per  pound  of  carbon  or  of 
fuel,  and  in  conjunction  with  this  formula,  certain  data  of  perfect 
combustion  which  may  be  obtained  from  Table  8. 

It  is  customary  and  proper  to  report  a  fuel  analysis  on  a  dry 
or  moisture  free  basis.  On  such  a  basis,  where  total  gas  weights 
are  desired,  the  water  vapor  in  the  flue  gases  resulting  from  the 
presence  of  moisture  in  the  fuel  should  be  computed  separately, 
and  in  the  proposed  method  of  determining  the  air  supplied  for 
combustion,  neglecting  the  moisture  content  of  such  air,  the 
results  obtained  are  in  terms  of  dry  fuel. 

Assuming  complete  combustion  of  the  hydrogen  present  in 
any  fuel,  the  water  vapor  content  of  the  flue  gases  from  this 
source  must  be  a  constant  weight  regardless  of  the  amount  of  air 
supplied  for  combustion.  This  weight  may  be  readily  determined 
from  the  percentage  of  hydrogen  in  the  fuel  (total  weight  per 
pound)  and  the  data  of  Table  8.  Obviously  then,  the  total  weight 
of  the  products  of  combustion  per  pound  of  dry  fuel  for  any 
amount  of  excess  air  must  equal  the  dry  products  of  combustion 
per  pound  as  given  by  formula  (27-^)  plus  the  constant  weight  of 

*  Less  unconsumed  C  in  ash. 

55 


the  water  vapor  formed  in  the  burning  of  the  hydrogen  content. 
Further,  the  total  weight  of  the  products  of  combustion  of  the  dry 
fuel  must  equal  the  weight  of  air  supplied  plus  the  weight  of  the 
fuel  which  is  burned,  and  appears  in  the  flue  gases.  Hence, 

Dry  products  per  pound  fuel-fH2O  from  H2  = 
Dry  air  supplied  per  pound  +  (Weight  fuel  in  gases)* 
or  \ 

J  Dry  air  supplied  per  pound  =  Dry  products  per  pound + 
\   H2O  from  H2— (Weight  fuel  in  gases)  / 

From  the  weight  of  air  supplied  as  so  determined,  and  the 
weight  theoretically  required  as  computed  from  Table  8  or  by 
formula  (25),  the  amount  of  excess  air  may  be  readily  found,  as 
may  be  the  ratio  of  air  supplied  to  that  theoretically  necessary, 
which  value,  assuming  complete  combustion,  is,  in  the  last  analysis, 
the  true  measure  of  the  efficiency  of  combustion. 

This  method,  as  stated,  necessitates  an  analysis  of  the  fuel  as 
well  as  of  the  flue  gases.  There  is  one  of  the  formulae  offered  for 
the  direct  computation  of  the  amount  of  air  supplied  for  combus- 
tion, based  on  a  volumetric  flue  gas  analysis  alone,  which,  while  it 
is  not  applicable  to  all  fuels,  will  give  reasonably  accurate  results 
for  most  solid  and  liquid  fuels,  and  for  this  reason  should  be 
discussed.  This  formula  as  ordinarily  given  is  i  \ 

1ST  sh*^ 

Dry  air  supplied  per  pound  C=     '  *      (28} 

where  the  symbols  represent  the  volumetric  percentages  of  carbon 
monoxide,  carbon  dioxide  and  nitrogen. 

This  formula  with  the  constant  3.032  is  derived  as  follows: 

The  last  term  of  formula  (27) 

7N, 

3(C03+CO) 

must  represent  the  weight  of  nitrogen  supplied  by  the  air,  plus  the 
weight  of  nitrogen  in  the  fuel  itself.  For  the  particular  fuel 
(coal  containing  one  per  cent  N2)  and  combustion  conditions  (20 
per  cent  excess  air)  from  which  the  constant  3.032  in  formula 
(28)  was  determined,  the  nitrogen  content  of  the  fuel  was  approxi- 
mately ¥Js  of  the  total  weight  of  nitrogen  in  the  dry  products 
of  combustion. 

*Ex.  in  the  case  of  coal  (i-Ash). 

56 


Since  the  nitrogen  is  76.85  per  cent  by  weight  of  the  air 
supplied  for  combustion,  the  weight  of  air  supplied  per  pound  of 
carbon  for  the  conditions  assumed  would  be  then 

"NT 

7  (N     —     *\ 
7  l    2     8oc/  3-032  N2 


.7685  x  3  (C02  +  C0)       (C02  +  C0) 

Since  the  correction  to  the  term  7  N2  will  vary  not  only 
with  the  nitrogen  content  of  the  fuel  but  also  with  the  amount 
of  excess  air  supplied,  and  for  this  reason  the  formula  must  be 
only  approximate  at  best,  it  would  perhaps  be  best  to  make  no 
attempt  to  correct  for  the  nitrogen  content  of  the  fuel,  in  which 
case  the  constant  instead  of  being  3.032  would  become  3.036, 
and  the  weight  of  air  supplied  per  pound  of  carbon  will  be 

7  N2  3.036  N2 

.7685x3(CO~+CO)  ~  (CO2  +  CO) 

For  the  determination  of  the  weight  of  dry  air  per  pound  of 
fuel  from  this  formula,  where  the  sulphur  content  of  the  fuel  is 
low,  this  value  may  be  obtained  by  multiplying  formula  (280)  by 
the  percentage  by  weight  of  carbon  in  the  fuel.  With  fuels  high 
in  sulphur  a  correction  may  be  made  to  modify  the  carbon 
content  as  in  the  case  of  the  determination  of  the  dry  products 
per  pound  of  fuel,  though  in  view  of  the  approximate  nature  of 
the  formula,  this  refinement  is  probably  not  warranted.  If  such 
modification  is  desired,  the  corrective  factor  instead  of  being 
based,  as  in  the  previous  case,  upon  the  ratio  of  SO2  to  CO2, 
should  be  based  on  the  weight  ratio  of  N2  jn  the  products  of 
combustion  of  one  pound  of  carbon  and  one  pound  of  sulphur 
respectively,  or  from  Table  8,  3.32  to  8.85.  With  such  correc- 
tion the  weight  of  dry  air  supplied  per  pound  of  fuel  would  be 

3-036  N2  s 

) 


(C02  +  C0)  2.667 


The  error  of  this  formula  will  depend,  as  stated,  not  only 
upon  the  nitrogen  content  of  the  fuel  but  also  upon  the  amount  of 
excess  air  supplied.  While  this  error  is  practically  negligible  for 
solid  and  liquid  fuels,  in  gaseous  fuels  it  is  sufficiently  large  to 
make  the  formula  useless.  The  reason  for  this  is  clear  if  we 
consider  blast  furnace  gas,  where  with  ordinarily  good  combus- 
tion, the  weight  of  nitrogen  in  the  fuel  itself  may  be  almost  as 

57 


great  as  that  in  the  air  introduced  for  combustion.    (See  example 
following.) 

Numerous  other  formulae  are  offered  for  the  determination 
of  the  ratio  of  air  to  that  required.  Such  formulae,  however,  are 
based  on  the  relations  of  nitrogen  and  oxygen  existing  in  the 
flue  gases,  and  are  incorrect  in  that  they  do  not  take  into  con- 
sideration the  fact  that  while,  with  most  fuels,  practically  all  of  the 
nitrogen  shown  was  introduced  with  the  air  supplied,  this  nitrogen 
is  composed  of  that  which  accompanied  the  oxygen  used  in  the 
combustion  of  carbon  and  appearing  as  carbon  dioxide  or  carbon 
monoxide,  and  that  which  accompanied  the  oxygen  used  in  the 
combustion  of  hydrogen,  this  latter  amount  of  oxygen  not 
appearing  in  the  flue  gas  analysis.  Hence  the  relation  of 
nitrogen  and  oxygen  in  the  dry  flue  gases  cannot  be  used  as 
indicative  of  similar  relations  existing  in  the  air  supplied. 
This  criticism  does  not  apply  to  formula  (28)  since  this  is  an 
expression  of  carbon-nitrogen  relations,  and  does  not  involve 
oxygen.  The  criticism  of  formula  (28)  as  to  nitrogen  content 
of  the  fuel  is  applicable  to  the  air  ratio  formulae  usually 
offered.  These  air  ratio  formulae  are  ordinarily  so  subject 
to  error  and  are  so  narrowly  applicable  that  they  are  not 
included  here. 

The  errors  resulting  from  the  proper  use  of  flue  gas  analysis 
in  the  computation  of  combustion  data  are  well  within  the  error 
of  boiler  testing  as  a  whole.  There  is,  however,  a  real  source  of 
possible  error  in  the  making  of  the  analyses,  and  in  practise 
there  are  several  features  that  should  be  carefully  watched  where 
accuracy  in  the  fuel  results  is  desired.  These  are  of  sufficient 
importance  to  warrant  discussion  and,  assuming  a  proper  design 
of  analysis  apparatus,  the  errors  to  be  guarded  against  may  be 
listed  as  follows  :  > 

First.  Care  should  be  taken  that  the  sample  of  gas  for 
analysis  is  an  average  sample.  This  is  the  feature  which  should 
be  most  carefully  watched  and  is  perhaps  the  most  difficult  of 
achievement.  No  hard  and  fast  rules  can  be  laid  down  for  the 
methods  of  obtaining  such  average  sample  and  it  is  largely  a 
question  of  common  sense.  The  sample  should  be  drawn  from 
the  main  body  of  the  gases  and  in  a  location  where  the  possibility 
of  dilution  through  air  infiltration  is  a  minimum. 

58 


Second.  Absorption  reagents  should  be  reasonably  fresh. 
Each  reagent  is  capable  of  absorbing  a  definite  amount  of  one  of 
the  constituent  gases,  this  amount  ordinarily  being  expressed  in 
terms  of  volume  of  the  absorbing  medium,  and  a.  check  should 
be  kept  on  the  total  absorption.  Where  solutions  are  weak  and 
absorption  is  not  accomplished  within  a  relatively  short  time, 
there  is  a  tendency  to  accept  the  absorption  as  complete,  which 
results  in  an  inaccurate  analysis. 

Third.  There  is  a  tendency,  particularly  in  the  case  of  inex- 
perienced operators,  toward  attempting  to  force  the  absorption. 
With  reasonably  fresh  solutions,  the  gas  should  be  brought  into 
contact  with  the  absorption  tubes  at  least  twice,  and  oftener  as 
the  solutions  become  weaker.  In  the  case  of  oxygen,  where, 
through  attempting  to  force  the  rapidity  of  the  analysis,  ab- 
sorption is  not  complete,  erroneous  results  both  as  to  oxygen 
and  carbon  monoxide  content  will  be  obtained  since  the  absorb- 
ing reagent  for  the  latter  will  also  absorb  oxygen. 

Fourth.  Analyses  should  be  completed.  Too  frequently  it  is 
assumed  that  the  carbon  dioxide  content  alone,  or  the  carbon 
dioxide  and  oxygen  content,  is  sufficient,  but  often  the  efficiency 
seemingly  indicated  by  a  high  carbon  dioxide  content  alone  would 
be  more  than  offset  by  the  fact  that  appreciable  amounts  of  carbon 
monoxide  were  present  and  not  analyzed. 

In  connection  with  the  completing  of  an  analysis,  it  is  perhaps 
well  to  warn  the  operator  not  to  start  an  analysis  with  the  fixed 
idea  that  the  sum  of  the  carbon  dioxide,  oxygen  and  carbon 
monoxide  must  total  to  a  fixed  amount.  This  sum  will  vary 
with  different  classes  of  fuel  and  to  an  extent  with  different  fuels 
of  the  same  class.  In  hand-firing  it  will  vary  in  samples  taken 
at  different  times  relative  to  the  firing  intervals,  as  the  volatile 
elements  are  consumed  to  a  greater  extent  directly  after  than 
before  firing.  How  great  the  variation  in  the  sum  of  these  three 
constituents  may  be  is  indicated  by  the  analyses  resulting  from 
the  combustion  of  different  fuels,  as  shown  in  the  examples  of 
computations  of  combustion  data  given  hereafter. 


59 


COMBUSTION  LOSSES 

WITH  the  methods  of  computing  combustion  data 
available,  it  is  now  possible  to  consider  the  losses 
which  occur  in  the  burning  of  fuel  under  a  steam 
boiler.  Certain  of  such  losses  are  not,  strictly  speaking,  com- 
bustion losses,  but  it  is  customary  to  consider  all  losses  together. 
The  results  of  the  computations  of  these  losses  constitute  the 
"heat  balance"  of  a  boiler  test  which  indicates  the  distribution  of 
losses.  Where  a  test  is  not  accompanied  by  such  a  heat  balance, 
or  at  least  by  sufficient  data  from  which  it  may  be  computed,  the 
results  should  not  ordinarily  be  accepted  as  absolutely  reliable. 

These  losses,  together  with  the  methods  of  their  computa- 
tions are : 

First.     Loss  due  to  the  moisture  contained  in  the  fuel. 

All  of  the  moisture  in  the  fuel  must  be  heated  from  atmos- 
pheric temperature  (or  from  the  temperature  of  the  fuel  where 
this  is  above  that  at  atmosphere)  to  2 1 2  degrees,  the  temperature 
at  which  steam  is  formed,  assuming  atmospheric  pressure,  and 
the  steam  so  formed  must  be  heated  to  the  temperature  of  the 
furnace  gases.  Since  in  passing  over  the  boiler  heating  surface 
the  temperature  will  ultimately  be  reduced  to  that  of  the  escaping 
gases,  the  first  and  last  temperatures  are  those  that  need  be  con- 
sidered. 

The  B.  t.  u.  loss  from  this  source  per  pound  of  fuel  may  be 
expressed 

Per  cent  Moisture  x  [(212 — /)  +  97o.4+48  (T — 212)]     (29) 

where  /=temperature  of  atmosphere  or  fuel, 

T=temperature  of  escaping  flue  gases, 
97O.4=latent  heat  of  evaporation  at  atmospheric  pressure, 
48=mean  specific  heat  of  superheated  steam  at  atmos- 
pheric pressure.     (In  reality  this  value  will  vary 
slightly  with  different  values  of  T,  but  the  varia- 
tion is  small  and  .48  may  be  taken  as  representing 
the  value  for  ordinary  exit  gas  temperatures.) 

In  the  case  of  gaseous  fuels  introduced  into  the  furnace  the 
moisture  content  already  exists  as  vapor.  The  temperature  of 
this  vapor  is  the  same  as  that  of  the  gas  with  which  it  is  mixed, 

60 


but  its  partial  pressure  is  below  that  corresponding  to  such 
temperature,  except  where  the  gas  is  saturated,  a  condition  which 
rarely  occurs.  Such  water  vapor,  then,  existing  at  a  temperature 
above  saturation,  or  above  the  temperature  corresponding  to  its 
partial  pressure,  is  in  reality  superheated  steam,  and  in  increasing 
its  temperature  to  that  of  the  escaping  gases  the  question  of 
the  expenditure  of  heat  in  changing  its  condition,  i.  e.,  latent 
heat  expenditure,  is  not  involved. 

The  loss  due  to  the  moisture  content  of  gaseous  fuels  will  be 
expressed  then 

Per  cent  moisture  x  .48  (T  —  /) 


Where  the  gaseous  fuel  is  introduced  into  the  furnace  at 
or  near  atmospheric  temperatures  the  specific  heat  of  the  water 
vapor  content  will  be  considerably  lower  than  0.48.  The  use  of 
this  value,  however,  as  the  mean  specific  heat  over  the  range 
t  —  T  will  lead  to  a  negligible  error  only.  ' 

Second.  Loss  due  to  moisture  formed  in  the  burning  of 
hydrogen. 

From  Table  8,  each  pound  of  hydrogen  burned  will  result  in 
the  formation  of  9  pounds  of  water  vapor.  Tyhis  moisture  must 
be  heated  as  in  the  case  of  the  moisture  in  the  fuel  and  the  loss 
may  be  expressed 

Percent  H2x  9  [(212—^  +  970.4+48  (T—  212)]    (j/) 

In  the  case  of  hydrogen,  since  water  is  an  actual  product  of 
combustion,  the  latent  heat  must  be  taken  into  consideration, 
regardless  of  the  fact  that  the  moisture  appears  in  the  products 
of  combustion  as  water  vapor,  and  whether  the  fuel  is  solid,  liquid 
or  gaseous. 

Third.     Loss  due  to  moisture  in  the  air* 

The  weight  of  water  vapor  per  pound  of  dry  air  may  be  de- 
termined from  readings  of  the  wet  and  dry  bulb  thermometers 
and  a  set  of  psychrometric  tables. 

This  weight  times  the  weight  of  dry  air  supplied  per  pound 
of  fuel,  as  determined  by  the  methods  which  have  been  indicated, 
will  give  the  total  moisture  in  the  air  supplied  per  pound  of  fuel 
(W).  Since  this  moisture  is  already  in  the  form  of  water  vapor, 


*  The  loss  due  to  moisture  in  the  air   is   frequently  not  computed  and  is 
included  with  the  unaccounted  losses. 

61 


as  in  the  case  of  the  moisture  content  of  gaseous  fuels,  the  question 
of  the  expenditure  of  heat  in  changing  its  condition  is  not  involved 
and  the  loss  from  this  source  will  be 

W  x  .48  x  (T— /)  (s») 

Fourth.  Loss  dtie  to  heat  carried  away  in  the  dry  chimney 
gases. 

The  weight  of  gas  per  pound  of  fuel  burned  (W)  may  be 
computed  by  the  methods  indicated.  In  the  case  of  solid  fuels 
when  the  weight  of  dry  gas  per  pound  of  carbon  as  given  by 
formula  (27)  is  multiplied  by  the  carbon  content  of  the  fuel,  the 
proper  value  of  the  carbon  for  use  is  the  percentage  of  carbon 
actually  burned  and  appearing  in  the  flue  gases,  i.  e.,  the  carbon 
content  corrected  for  any  unconsumed  carbon  in  the  ash  and 
refuse. 

The  heat  lost  in  the  dry  chimney  gases  then,  is  measured 
by  this  weight  of  gas  (W)  and  the  difference  between  the 
temperature  of  the  escaping  gases  and  that  of  the  atmosphere. 
It  may  be  expressed 

W  (T— /)  x  .24  (33} 

where  .24  is  taken  as  the  mean  specific  heat  of  the  gas  between 
these  temperature  limits.  Since  this  specific  heat  will  vary  with 
the  temperature  of  the  escaping  gases  and  with  their  composition, 
it  would  be  well  to  compute  its  value  where  the  most  accurate 
results  are  desired.  The  value  .24,  though  probably  somewhat 
low,  is,  however,  ordinarily  accepted. 

Fifth.     Loss  due  to  the  incomplete  combustion  of  carbon. 

This  loss  may  be  expressed 

CO 


C02  -f  CO 


x   C   x    10160  (34} 


in  which  C  is  the  weight  of  carbon  which  is  burned  and  appears  in 
the  flue  gases,  i.  e.y  corrected  for  solid  fuels,  as  in  the  case  of  the 
proceeding  loss,  for  such  unconsumed  carbon  as  appears  in  the 
ash.  The  constant  10160  represents  the  number  of  heat  units 
generated  in  burning  one  pound  of  carbon  in  carbon  monoxide 

CO 

to  carbon  dioxide.    The  term  —  —  —  ,  in  which  the  symbols 

-f-  \~>\j 


62 


represent  the  volumetric  percentages  of  the  constituents  as 
shown  by  analysis,  is  an  expression  denoting  the  weight  of  the 
carbon  present  in  the  carbon  monoxide  constituents,  and  perhaps 
needs  explanation. 

From  formula  (27),  the  weight  of  carbon  monoxide  in  the 
flue  gas  is  given  by 

7  CO 
3  (C02  +  CO) 

If  this  expresses  the  weight  of  carbon  monoxide  in  terms  of 
volumetric  percentages  of  the  constituents,  obviously  the  weight 
of  carbon  in  the  carbon  monoxide  must  be  f  of  this  amount  or 

CO 
C02  +  CO' 

Sixth.     Loss  due  to  carbon  appearing  in  unconsumed  refuse. 

This  loss  may  ordinarily  be  determined  only  in  the  case  of 
solid  fuels.  It  is  expressed 

C   X    C     x    14600  1*5) 

IOO 

where  £— weight  of  ash  per  pound  of  fuel, 

C=per  cent  of  unconsumed  combustible  matter  in 

the  ash, 
£xC— weight  of  unconsumed  carbon  in  terms  of  total 

carbon  per  pound  of  fuel. 

The  unconsumed  combustible  matter  in  the  refuse  is  assumed 
to  be  entirely  carbon  for  which  14600  B.  t.  u.  per  pound  is  taken 
as  the  approximate  heat  value.  This  assumption  will  give  rise  to 
an  error  which  is  negligible. 

Seventh.     Radiation  and  unaccounted  losses. 
These  losses,  which  are  either  impossible  or  impracticable  to 
measure,  include: 

(a)  Radiation  loss,  which  in  terms  of  percentage  will  vary  with 
the  size  of  the  unit,  the  condition  of  the  setting  and  like 
factors. 

(ft)     Losses  due  to  unburned  volatile  hydrocarbons. 

(c)     Loss  due  to  the  combination  of  carbon  and  moisture,  with  the 
consequent  formation  of  hydrogen  (C  +  H2O  =  CO  +  H2), 
which  may  or  may  not  be  burned.     This  action  may  occur 
when  moist  fuel  is  thrown  on  an  incandescent  fuel  bed. 

(if)    Other  losses  not  accounted  above. 

63 


The  total  of  the  losses  under  item  seven  is  taken  as  the  differ- 
ence between  100  per  cent  and  the  boiler  efficiency  plus  the  sum 
of  the  six  losses  as  computed. 

The  actual  computations  of  two  typical  heat  balances  are  given 
in  examples  hereafter. 

Of  the  losses  listed  which  can  be  computed  the  first,  second 
and  third  items  are  only  to  an  extent  controllable.  Since 
the  moisture  content  of  all  fuels  and  of  air,  and  the  hydrogen 
content  of  most  fuels  must  be  accepted  as  found,  the  only  manner 
is  which  these  losses  may  be  kept  at  a  minimum  for  a  given 
fuel  is  by  the  reduction  of  the  exit  gas  temperature  to  the  lowest 
possible  or  practicable  figure.  Assuming  proper  combustion, 
the  exit  gas  temperature  is  a  function  of  the  heat  absorbing 
ability  of  the  boiler,  and  is  thus  rather  a  question  of  boiler  design 
than  of  combustion  proper.  If,  on  the  other  hand,  the  efficient 
absorbing  power  of  the  boiler  is  assumed,  these  three  losses  are 
controllable  to  the  extent  that  exit  gas  temperatures  are  dependent 
upon  combustion. 

The  fourth  loss  is  more  truly  a  combustion  loss  though  since 
it  is  affected  by  exit  gas  temperatures  this  too  is  dependent  on 
boiler  design.  Obviously  with  a  given  fuel,  and  for  a  given  exit 
gas  temperature,  the  greater  the  gas  weight,  i.  e.,  the  greater  the 
excess  air,  the  greater  the  loss  of  heat  in  the  chimney  gases. 
This  loss  is  kept  at  a  minimum  when  complete  combustion  is 
made  to  approach  perfect  combustion. 

The  fifth  loss  is  entirely  a  combustion  loss  and  is  to  be 
prevented  only  by  the  admission  of  sufficient  air  for  complete 
combustion  and  in  a  manner  that  such  complete  combustion  is 
assured.  In  endeavoring  to  bring  about  such  conditions  the  ten- 
dency is  toward  the  introduction  of  too  great  an  amount  of  air,  in 
which  case  the  carbon  monoxide  loss  will  be  reduced  or  prevented 
at  the  expense  of  a  loss  resulting  from  the  fourth  source.  It  is 
to  be  remembered  that  while  the  absence  of  carbon  monoxide  in 
the  flue  gases  indicates  complete  combustion,  it  does  not  of  neces- 
sity indicate  efficient  combustion. 

The  sixth  loss,  which  can  only  be  determined  with  solid  fuels, 
is  not  properly  speaking  a  combustion  loss  and  is  the  result  of 
the  physical  factors  entering  into  the  design  of  furnaces,  stokers 
or  grates,  and  in  the  operation  of  the  apparatus.  Assuming 

64 


the  best  of  design  this  loss  is  minimized  through  proper 
operation. 

It  will  be  noted  from  the  foregoing  that  the  two  main  factors 
upon  which  the  extent  of  all  combustion  losses  depend  are  the 
amount  of  air  supplied  for  combustion  and  the  temperature  of 
the  gases  leaving  the  boiler  heating  surfaces.  The  factor  of  air 
supply  can,  within  limits,  be  controlled,  but  if  we  assume  the 
ability  of  a  boiler  to  absorb  heat  efficiently,  the  factor  of  exit 
gas  temperature  can  only  be  controlled  to  the  extent  that  it  is 
dependent  upon  air  supply.  In  view  of  this  fact  the  effect  of 
air  supply  on  exit  gas  temperature  must  be  considered. 

On  first  thought  it  would  appear  that  since  large  quantities 
of  excess  air  introduced  into  the  furnace  would  reduce  the 
temperature  of  the  products  of  combustion  before  the  boiler 
heating  surfaces  are  encountered,  such  dilution  would  result  in 
lower  exit  gas  temperatures  and  it  is  of  course  entirely  possible  to 
carry  this  dilution  to  the  products  of  combustion  in  the  furnace 
to  a  point  where  such  a  decrease  in  ultimate  temperature  would 
result.  In  practise,  however,  even  where  the  amounts  of  excess  air 
correspond  to  the  most  inefficient  combustion,  this  excess,  instead 
of  decreasing,  tends  to  increase  the  exit  gas  temperature. 

The  common  explanation  of  this  apparent  phenomenon  is 
that  the  excess  air  in  passing  through  and  mingling  with  the 
actual  products  of  combustion  absorbs  heat  from  such  products 
more  readily  than  will  the  boiler  heating  surfaces,  and  a  con- 
siderable portion  of  the  heat  so  absorbed  is  carried  off  in  the 
escaping  gases.  Such  a  statement  offers  by  far  the  simplest 
explanation,  and  one  which  accounts  for  a  part  at  least  of  the 
increase  of  exit  gas  temperature  with  an  increase  of  excess  air. 
The  other  factor  leading  to  such  a  result  is  dependent  upon 
heat  transfer  rates,  difference  in  temperature  between  the  gases 
and  the  absorbing  surface,  the  percentage  of  total  heat  absorbed 
through  radiation  and  the  percentage  of  total  absorption  through 
convection.  Any  attempt  to  explain  the  high  exit  temperatures 
accompanying  large  amounts  of  excess  air  on  such  a  basis  leads 
to  a  complication  of  theories  that  are  not  within  the  scope  of 
the  present  article. 

If  we  accept  the  foregoing  as  correct,  it  is  obvious  that  the 
stack  loss  due  to  excess  air  will  increase  with  such  excess,  not 

65 


only  because  additional  amounts  of  air  must  be  heated  from 
atmospheric  temperature  to  that  of  the  escaping  gases,  but  also 
because  the  ultimate  temperature  will,  within  ordinary  limits,  be 
higher  as  the  amount  of  excess  is  increased,  the  two  factors  thus 
combining  to  increase  the  possible  loss  under  item  four,  as  listed 
previously. 

The  effect  of  incomplete  combustion  in  the  furnace  may  be 
either  to  reduce  or  increase  exit  gas  temperatures. 

If  the  combustion  of  a  given  fuel  is  not  completed  in  the 
furnace  before  the  combustible  gases  come  into  contact  with  the 
boiler  heating  surfaces,  the  temperature  evolved  in  the  furnace, 
and  hence  the  temperature  of  the  products  of  combustion,  will 
be  less  than  if  such  combustion  were  complete.  If  such  un- 
consumed  or  partially  consumed  gases  pass  from  the  boiler  and 
up  the  stack  without  encountering  somewhere  in  the  setting 
sufficient  additional  oxygen  for  the  completion  of  combustion,  or 
temperatures  under  which  combination  resulting  in  further 
combustion  will  take  place,  the  result  on  the  ultimate  flue  gas 
temperature  would  be  to  reduce  it  below  what  it  would  be  if 
combustion  had  been  complete  in  the  furnace.  If,  on  the  other 
hand,  these  partially  consumed  gases  encounter  at  some  point  in 
their  passage  over  the  boiler  heating  surface  sufficient  oxygen 
for  continued  combustion  with  a  temperature  above  the  ignition 
point,  such  combustion  will  occur.  In  boiler  practise  this  is 
known  as  delayed  or  secondary  combustion,  and  ordinarily  will 
take  place  at  such  a  point  within  the  boiler  setting  as  to 
appreciably  increase  the  temperature  of  the  exit  gases  above 
that  which  would  result  from  complete  combustion  in  the  furnace. 


66 


SMOKE 

THOUGH  there  is  perhaps  no  phase  of  combustion  that 
has  been  so  fully  discussed  as  that  which  results  in  the 
production  of  smoke,  the  common  understanding  of  the 
loss  from  this  source  is  at  best  vague,  and  based  in  part  at  least 
on  misconception.    For  this  reason  a  brief  consideration  of  smoke 
is  included  here,  regardless  of  the  amount  of  data  on  the  subject 
available  elsewhere. 

Of  the  numerous  and  frequently  unsatisfactory  definitions  of 
smoke  that  have  been  offered,  that  of  the  Chicago  Association  of 
Commerce  Committee  in  its  report  on  "Smoke  Abatement  and 
the  Electrification  of  Railway  Terminals  in  Chicago,"  is  perhaps 
the  best.  This  report  defines  smoke  as  "the  gaseous  and  solid 
products  of  combustion,  visible  and  invisible,  including  .... 
mineral  and  other  substances  carried  into  the  atmosphere  with 
the  products  of  combustion." 

From  the  standpoint  of  combustion  loss  it  is  necessary  to 
lay  stress  on  the  term  "visible  and  invisible."  The  common  con- 
ception of  the  extent  of  loss  is  based  on  the  visible  smoke,  and 
such  conception  is  so  general  that  practically  all  if  not  all  smoke 
ordinances  are  based  on  visibility,  density  or  color  of  escaping 
stack  gases.  As  a  matter  of  fact,  the  color  of  smoke,  which  is 
imparted  to  the  gases  by  particles  of  carbon,  cannot  be  taken  as 
an  indication  of  the  stack  loss.  The  invisible  or  practically 
colorless  gases  issuing  from  a  stack  may  represent  a  combustion 
loss  many  times  as  great  as  that  due  to  the  actual  carbon  present 
in  the  gases,  and  but  a  small  amount  of  such  carbon  is  sufficient 
to  give  color  to  large  volumes  of  invisible  gases  which  may  or 
may  not  represent  direct  combustion  losses.  A  certain  amount 
of  color  may  also  be  given  to  the  gases  by  particles  of  flocculent 
ash  and  mineral  matter,  neither  of  which  represents  a  combustion 
loss.  The  amount  of  such  material  in  the  escaping  gases  may 
be  considerable  where  stokers  of  the  forced  draft  type  are  used 
and  heavy  overloads  are  carried. 

The  carbon  or  soot  particles  in  smoke  from  solid  fuels  is  not 
due  to  the  incomplete  combustion  of  the  fixed  carbon  content 
of  the  fuel.  They  result  rather  from  the  non-combustion  or 
incomplete  combustion  of  the  volatile  and  heavy  hydrocarbon 

67 


constituents,  and  it  is  the  wholly  or  partially  incomplete  com- 
bustion of  these  constituents  that  causes  smoke  from  all  fuels, 
solid,  liquid  or  gaseous. 

If  the  volatile  hydrocarbons  are  not  consumed  in  the  furnace, 
and  there-  is  no  secondary  combustion,  there  will  of  course  be  a 
direct  loss  resulting  from  the  non-combustion  of  these  con- 
stituents. While  certain  of  these  unconsumed  gases  may  appear 
as  visible  smoke,  the  loss  from  this  source  cannot  be  measured 
with  the  ordinary  flue  gas  analysis  apparatus,  and  must  of 
necessity  be  included  with  the  unaccounted  losses. 

Where  the  combustion  of  the  hydrocarbon  constituents  is  in- 
complete a  portion  of  the  carbon  component  ordinarily  appears 
as  soot  particles  in  the  smoke.  In  the  burning  of  hydrocarbons 
the  hydrogen  constituent  unites  with  oxygen  before  the  carbon  ; 
for  example,  in  the  case  of  ethylene  (C2H4) 


If  after  the  hydrogen  is  "satisfied"  there  is  sufficient  oxygen 
present  with  which  that  carbon  component  may  unite,  and 
temperature  conditions  are  right,  such  combination  will  take 
place  and  combustion  will  be  complete.  If  on  the  other  hand 
sufficient  oxygen  is  not  present,  or  if  the  temperature  is  reduced 
below  the  combining  temperature  of  carbon  and  oxygen,  regard- 
less of  the  amount  of  oxygen  present,  the  carbon  will  pass  off 
unconsumed  as  soot. 

The  direct  loss  from  unconsumed  carbon  passing  off  in  this 
manner  is  probably  rarely  in  excess  of  one  per  cent  of  the  total 
fuel  burned  even  in  the  case  of  the  densest  smoke.  The  loss 
due  to  unconsumed  or  partially  consumed  volatile  hydrocarbons, 
on  the  other  hand,  though  not  indicated  by  the  appearance  of 
the  gases  issuing  from  a  stack,  may  represent  a  very  appreciable 
percentage  of  the  total  fuel  fired. 

While  the  loss  represented  by  the  visible  constituents  of 
smoke  leaving  a  chimney  may  ordinarily  be  considered  negligible, 
there  is  a  loss  due  to  the  presence  of  unconsumed  carbon  and 
tarry  hydrocarbons  in  the  products  of  combustion  which,  while 
not  a  direct  combustion  loss,  may  result  in  a  much  greater  loss 
in  efficiency  than  that  due  to  visible  smoke.  These  constituents 
adhere  to  the  boiler  heating  surfaces,  and  acting  as  an  insulating 

68 


layer  greatly  reduce  the  heat  absorbing  ability  of  such  surfaces. 
From  the  foregoing  it  is  evident  that  the  stack  losses  indi- 
cated by  smoke,  whether  visible  or  invisible,  result  almost 
entirely  from  improper  combustion.  Assuming  a  furnace  of 
proper  design  and  fuel  burning  apparatus  of  the  best,  there  will 
be  no  objectionable  smoke  where  there  is  good  combustion.  On 
the  other  hand  a  smokeless  chimney  is  not  necessarily  indicative 
of  proper  or  even  of  good  combustion.  Large  quantities  of 
excess  air  in  diluting  the  products  of  combustion  naturally  tend 
toward  a  smokeless  stack,  but  the  possible  combustion  losses 
corresponding  to  such  an  excess  air  supply  have  been  shown. 


GENERAL  CONCLUSIONS 

IN  view  of  the  great  number  of  factors  involved  in  the  com- 
bustion of  any  fuel,  and  the  great  variation  in  the  charac- 
teristics not  only  of  different  classes  of  fuel,  but  of  different 
fuels  of  the  same  class,  it  is  obvious  that  the  specific  require- 
ments for  the  proper  combustion  of  an  individual  fuel  must  be 
considered  as  a  distinct  problem.  It  is  possible,  however,  from 
the  foregoing,  to  draw  certain  general  conclusions  as  to  the  com- 
bustion requirements  of  any  fuel,  whether  solid,  liquid  or  gaseous, 
and  since  such  conclusions  form  the  basis  of  the  design  of  all 
combustion  apparatus,  they  are  worthy  of  careful  note. 

These  general  requirements  of  proper  combustion  may  be 
summarized  as  follows : 

First.  The  admission  of  an  air  supply  such  as  will  assure 
sufficient  oxygen  for  complete  combustion. 

Second.  Since  complete  combustion  is  not  of  necessity 
efficient  combustion,  it  must  be  secured  without  permitting  the 
dilution  of  the  products  of  combustion  with  excess  air.  It 
follows  then,  that 

Third.  The  air  supply  should  be  admitted  at  the  proper 
time  and  in  such  a  manner  that  the  oxygen  of  the  air  comes  into 
free  and  intimate  contact  with  the  combustible  substances  of 
the  fuel.  In  the  case  of  solid  fuels  this  means  not  only  into 
contact  with  the  solid  particles  of  the  oxidizable  substances, 
but  also  with  the  combustible  gases  as  they  are  distilled  from 
the  fuel. 

Fourth.  The  gases  must  be  maintained  at  a  temperature  at 
or  above  their  ignition  point  until  combustion  is  complete. 
Theoretically,  as  has  been  indicated,  the  most  efficient  com- 
bustion is  that  resulting  in  the  maximum  temperature  possible. 
In  practice,  there  are  frequently  factors  which,  from  the  stand- 
point of  practical  operating  efficiency,  make  it  advisable  to  keep 
furnace  temperatures  somewhat  below  those  which  could  be 
obtained  were  this  the  sole  factor  involved. 

Fifth.  An  additional  requirement  which  has  to  do  with  the 
physical  rather  than  the  chemical  aspect  of  combustion  is  that 
proper  provision  must  be  made  for  the  expansion  of  gases  during 
the  period  of  their  combustion. 

70 


In  considering  combustion  it  is  necessary,  though  perhaps 
difficult  for  the  average  boiler  user,  to  distinguish  between  the 
purely  chemical  changes  that  accompany  oxidization  and  the 
purely  physical  aspect  of  the  later  transformation  of  heat  energy 
in  the  passage  of  the  products  of  combustion  through  the  boiler, 
i.  e.y  the  absorption  of  heat  by  the  boiler  from  such  gases.  The 
efficiency  of  combustion  is  thus  independent  of  the  ability  of  the 
boiler  under  which  combustion  takes  place  to  absorb  heat,  and 
in  the  requirements  of  proper  combustion  just  summarized  such 
ability  is  either  assumed  or  neglected. 

From  the  general  conclusions  drawn  it  would  seem  perhaps 
a  simple  matter  to  meet  the  requirements  of  proper  combustion. 
Unfortunately,  however,  such  is  not  the  case  and  it  is,  as  stated 
heretofore,  the  physical  and  mechanical  details  encountered  in 
attempting  to  fulfill  such  requirements  that  render  the  problem 
of  proper  combustion  difficult.  Assuming  proper  furnace  form 
and  adequate  combustion  temperatures,  the  problem  is  solely 
one  of  air  admission  and  admixture.  The  factors  entering  into 
the  problem  and  the  methods  used  to  bring  about  the  desired 
results  are  so  widely  varied  for  different  fuels,  that  it  is  neces- 
sary, as  stated,  to  consider  each  class  of  fuel  specifically  for  any 
but  the  most  general  statements. 


THE  COMPUTATION  OF  COMBUSTION 

DATA 

THE  methods  of  computing  combustion  data  as  discussed 
in  the  foregoing,  and  the  very  widely  differing  data  result- 
ing from  the  combustion  of  different  classes  of  fuel,  i.  e., 
the  wide  variation  in  possible  or  probable  flue  gas  analyses,  products 
of  combustion  and  air  supplied  per  pound  of  fuel  for  different 
combustion  conditions  are,  to  the  writer's  mind,  best  illustrated 
by  example. 

.  For  this  reason  typical  examples  of  the  different  classes  of 
fuel  used,  commonly  for  the  production  of  heat  under  steam 
boilers  are  considered  in  the  following.  Except  in  the  case  of 
coal  where  the  analyses  vary  over  a  wide  range,  the  analyses 
of  the  fuels  taken  are  sufficiently  near  an  average  to  allow  the 
results  to  be  plotted  in  such  manner  that  for  a  given  flue  gas 
analysis  (i.  e.,  per  cent  CO2),  the  weight  of  the  products  of  com- 
bustion and  the  amount  of  excess  air  corresponding  to  such 
analysis,  may  be  determined  directly  for  the  specific  class  of  fuel 
considered  with  a  degree  of  accuracy  sufficient  for  approximate 
work.  Such  graphic  representations  are  therefore  included. 

COAL 

Given  a  coal  having  the  following  ultimate  analysis : 

Per  Cent 

Carbon       .  ......     .     ...     .  79.86 

Hydrogen.  ...     .     .    '.     .     .     .  5.02 

Oxygen      .  .     .     .     .     .     ...    .     .     .  4-27 

Nitrogen    .  .     ....     ....  1.86 

Sulphur     .  .     ,     .     .     ....     .  1. 1 8 

Ash       .     .  .     .     .    >'.';     .     .     .     .  7.81 


100.00 

Moisture 2.90  per  cent 

B.  t.  u.,  per  pound I4351 

72 


With  perfect  combustion  the  oxygen  and  air  required,  and 
the  products  of  combustion  per  pound  of  coal  will  be  as  follows : 


Weight 
per  Pound 
Coal 
Pounds 

Required  —  Pounds 

•Products  of  Combustion—  Pounds  per  Pound  Coal 

O2 

Air 

C02 

02 

N3 

H20 

SO, 

c 

H2 
02 

N2 
S 
Ash 

.7986 
.0502 
.0427 
.0186 
.OIl8 
.0781 

2.130 
.402 

9-2OO 
1-735 

2.929 

.043 

7.070 
1-333 

•452. 

.   .   . 

.019 
•039 

.012 

.051 

.024 

i  .0000 
,„   O2  in  Coal 

2.544 
-.043 

10.986 
^  .186* 

2.929 

•043 
-•043 

8.461 
—  143* 

452 

.024 

SO2  as  CO2 

2.501 

IO.8OO- 

2.929 
.024 

.000 

8.318 

•452 

.024 
.024 

2.501 

10.800 

2-953 

.000 

8.318 

452 

.000 

*Air  and  N2  equivalents  of  O3  in  coal. 

The  weight  of  air  theoretically  required  for  the  combustion 
of  one  pound  of  coal  is  then  10.800  pounds.  For  each  20  per 
cent  in  excess  of  this  amount  (i.e.,  each  2.160  pounds  above 
10.800)  there  will  appear  in  the  products  of  combustion 

2.i6ox.23i5=   .500  pounds  O 2 
2.160  x  .7685=1.660  pounds  N2 

and  the  weights  of  the  products  of  combustion  per  pound  of  coal 
for  varying  amounts  of  excess  air  will  be : 

TABLE  A 


'    -  - 


Weight 
Products 
Perfect 
Combustion 

Weight  Products  —  Varying  Amounts  of  Excess  Air—  Pounds 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

100  Per  Cent 

C02 
02 

N2 
H2O 

2-953 
,OOO 
8.318 

•452 

2-953 
.500 
9.978 
.452 

2-953 

I.OOO 

11.638 

.452 

2-953 

1.500 

13.298 
.452 

2-953 

2.000 
14.958 
•452 

2-953 
2.500 

16.618 
•452 

11.723 

13-883 

16.043 

18.203 

20.363 

22.523 

73 


Expressed  in  terms  of  percentage  weight,  these  values  are : 

TABLE  B 


Per  Cent 
Weight 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Products—  Varying  Amounts  of  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 

25.190 

21  270 

18.407 

16.223 

14.502 

I3.III 

02 

.000 

3.602 

6.233 

8.240 

9.821 

II.  IOO 

N2 

70.955 

71.872 

72-543 

73-054 

73-458 

73-782 

H20 

3.855 

3-256 

2.817 

2.483 

2.219 

2.007 

100.000 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

Expressed  in  terms  of  percentage  weight  of  dry  products  of 
combustion  these  values  are : 


TABLE  c 


Per  Cent 
Weight  Dry 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Dry  Products—  Varying  Amounts  of  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 

26.2OO 
.000 
73-800 

21.987 

3-723 
74.290 

18.940 
6.414 
74.646 

16.636 
8.450 
74.914 

14.831 
10.044 
75-125 

I3-380 
11.327 

75-293 

If  we  convert  these  percentages  by  weight  of  the  dry 
products  of  combustion  into  terms  of  percentage  by  volume  after 
the  method  given  on  page  19,  the  values  as  given  in  Table  C 
become : 

TABLE    D 


Per  Cent 
Volume 
Dry  Products 
Perfect 
Combustion 

Per  Cent  Volume  Dry  Products  —  Varying  Amounts  of  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

CO2 
02 

N2 

18.428 
.OOO 
81.572 

15.285 

3-559 
81.156 

I3-057 
6.080 
80.863 

11.396 
7.960 
80.644 

IO.IIO 

9-4I5 

80.475 

9.085 

10-575 
80.340 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

For  the  purpose  of  comparing  the  results  as  computed  as 
above  with  those  obtained  through  the  use  of  the  combustion 


74 


formulae  which  have  been  discussed,  assume  that  the  coal  is 
burned  with  40  per  cent  excess  air  and  the  flue  gas  analysis  by 
volume  shows  1  3.057  per  cent  CO  2,  6.080  per  cent  O2  and  80.683 
per  cent  N2. 

The  weight  of  dry  products  of  combustion  per  pound  of  carbon 
will  be,  from  formula 


ii  x  13.057+8  x  6.080+7  x  80.863 

3x13.057  =I9'359  pounds 

Multiplying  this  value  by  the  weight  of  carbon  per  pound  of 
dry  coal,  we  have  as  the  weight  of  dry  products  per  pound  of  dry 
coal 

19.359  x  .7986=15.460  pounds 

as  against  a  value,  in  Table  A,  of 

16.043  —  -4S2==IS'S9l  pounds 

an  error  of  0.131  pounds,  or  0.84  per  cent.  If  the  carbon  weight 
is  corrected  for  the  sulphur  equivalent  as  explained  on  page  54, 
the  value  of  C  becomes 

7986+(.oi2*-r-i.833)=.8o5i 

and  the  weight  of  dry  products  of  combustion  per  pound  of 
dry  coal  becomes 

.8051  x  19.359=15.586  pounds 

which  checks  with  the  value  of  Table  A  within  0.03  per  cent. 

The  total  weight  of  gas  per  pound  of  coal  fired  will  be  the 
sum  of  the  dry  products  per  pound  of  dry  coal,  the  water  vapor 
from  the  hydrogen,  and  the  weight  of  moisture  per  pound  of  coal, 

or  15.591  +  .452  +  .029=  16.072  pounds 

The  weight  of  dry  air  supplied  per  pound  of  carbon,  from 
formula  (28),  will  be 

3.036  x  80.863 


I3-057 


=  18.802  pounds 


*Weight  of  S  used  in  computing  SO2. 

75 


The  weight  of  dry  air  supplied  per  pound  of  coal,  using  the 
actual  carbon  weight,  will  be 

18.802  x  .7986=15.015  pounds 

while  the  weight  using  the  carbon  weight  corrected  for  the 
sulphur  equivalent  (in  this  case  the  ratio  of  the  nitrogen  in  the 
air  supplied  for  the  combustion  of  carbon  and  sulphur  to  CO2  and 
SO  2  respectively)  will  be 

18.802  x  [.7986-f-(.oi2-^2.667)]=i 5.100  pounds 

The  actual  weight  of  air  supplied  per  pound  of  dry  fuel  will 
be  the  total  products  of  combustion  per  pound  of  dry  coal,  less 
the  weight  per  pound  which  is  burned  and  appears  in  such 
products,  or,  from  Table  A  and  the  weight  of  ash  as  given  by 
the  analysis 

16.043 — (l — .078)=  1 5. 12 1  pounds 

For  this  particular  coal  then,  the  errors  above,  using  the  uncor- 
rected  and  the  corrected  values  of  carbon  as  applied  to  formula 
(28),  are  0.70  per  cent  and  0.14  per  cent  respectively. 

Formulae  (28 ',  28 a  and  28 b)  will,  as  stated,  give  results  within 
reasonably  accurate  limits,  with  fuels  having  a  low  nitrogen  con- 
tent, the  error  varying  with  the  percentage  of  nitrogen  and  with 
the  amount  of  air  used  for  combustion.  With  fuels  of  high 
nitrogen  content,  the  error  may  be  as  great  as  80 — 90  per  cent 
(see  Blast  Furnace  Gas)  and  for  such  fuels  these  formulae  are 
not  to  be  relied  upon. 

The  heat  of  combustion  per  pound  of  dry  coal  computed 
from  formula  (4)  will  be 

0427 
I46oox  .7986  +  62000  (.0502 g-^)  +  405ox  .0118 

=  14492  B.  t.  u. 

as  against  the  calorimetrically  determined  value  14351  B.  t.  u., 
an  error  of  0.99  per  cent. 

To  indicate  the  amount  of  possible  error  with  high  sulphur 
fuels,  in  the  determination  of  the  dry  products  of  combustion 
per  pound  of  fuel  from  formula  (27)  where  the  carbon  content  is 
not  corrected  for  the  sulphur  equivalent,  let  us  assume  a  coal 
having  the  analysis  given  below.  The  weight  of  oxygen  and  air 

76 


theoretically  required,  and  the  weight  of  the  products  of  perfect 
combustion  per  pound  of  dry  coal  will  be  as  follows : 


Weight 
per  Pound 
Coal 
Pounds 

Required—  Pounds  . 

Products  of  Combustion  —  Pounds  per  Pound  Coal 

02 

Air 

CO, 

02 

N2 

H2O 

SO, 

c 

H2 
02 

N2 
S 
Ash 

.6125 
.0448 
.1062 
.0100 

.0442 
.1823 

I-6335 
.3584 

7.0560 
L5483 

2.2460 

•   •  - 

54225 
1.1898 

.4032 

.   .   . 

.1062 

.0100 

.1467 

.0442 

.1909 

.      .      . 

.0884 

O2  in  Coal  . 

2.0361 
.1062 

8.7952 
4588 

2.2460 

.1062 
.1062 

6.7690 

•3526 

.4032 

.0884 

SO2  as  CO2 

1.9299 

8.3364 

2.2460 
.0884 

.0000 

6.4164 

.4032 

.0884 
.0884 

1.9299 

8.3364 

2.3344 

.0000 

6.4164 

.4032 

.0000 

The  air  required  per  pound  of  dry  coal  for  perfect  combustion 
is  thus  8.3364  pounds.  If  we  assume  the  coal  to  be  burned  with 
20  per  cent  excess  air,  there  will  appear  in  the  products  of  com- 
bustion, in  addition  to  the  weights  just  given, 

1.6673  x  .2315=  .3860  pounds  O2 
1.6673  x  .7685  =  1.2813  pounds  JN2 

With  20  per  cent  excess  air  then,  the  weight  of  the  pro- 
ducts of  combustion  per  pound  of  dry  coal,  these  weights 
expressed  in  terms  of  percentage  weight,  expressed  in  terms 
of  percentage  weight  of  dry  products,  and  expressed  in  terms  of 
percentage  volume  of  dry  products,  are  as  follows : 


Weight 
Products 
Pounds 

Per  Cent 
Weight 
Products 

Per  Cent 
Weight 
Dry  Products 

Per  Cent 
Volume 
Dry  Products 

C02 

°2 

N2 
H2O 

2-3344 
.3860 

7.6977 
.4032 

21.572 
3.567 

7LI35 
3.726 

22.407 
3.705 

73-888 

15.603 

3-547 

80.850 

10.8213 

IOO.OOO 

IOO.OOO 

IOO.OOO 

77 


Under  the  assumed  conditions,  the  weight  of  dry  gas  per  pound 
of  carbon  will  be  from  formula  (27) : 

II  x  15.603  +  8x3.547+7x80.850 

3x15.603  -=16.3635  pounds 

Multiplying  this  value  by  .6125,  the  weight  of  carbon  per  pound 
of  dry  coal,  we  have  as  the  dry  products  per  pound 

16.3635  x  .6125  —  10.022  pounds 
as  against  the  computed  value  above 

10.8213 — .4032—10.418  pounds 

an  error  of  approximately  4.0  per  cent.  If,  on  the  other  hand, 
the  weight  of  carbon  is  corrected  for  the  sulphur  equivalent,  we 
have 

16.3635  x  [.6i25+(.0442-^i.833)]=io.4i7  pounds 
which  value  checks  with  the  computed  weight. 

WOOD 
Given  a  wood  (pine)  having  the  following  ultimate  analysis 

Per  Cent 

Carbon  .     .  '. ...     .     ...     ,     .  ,  .     .     50.31 

Hydrogen  .     .     .     .     •      .     *     •     •     •       6.20 

Oxygen       ,..;    ....    ..     .    i.     43.08 

Nitrogen     , .04 

Ash 37 


100.00 

Moisture 46.10  per  cent 

Heat  value  per  pound  dry  wood,  B.  t.  u.      9153 

78 


With  perfect  combustion  the  oxygen  and  air  required  per 
pound  of  dry  wood  and  the  products  of  combustion  per  pound 
will  be  as  follows: 


Weight 
Per  Pound 
Wood 
Pounds 

Required  —  Pounds 

Products  of  Combustions-  Pounds  Per  Pound  Wood 

02 

Air 

CO, 

02 

N, 

H,O 

c 

H2 
02 

N2 
Ash 

•5031 
.0620 
.4308 
.0004 
.0037 

1-342 
.4960 

5.796 
2.143 

1.845 

.   .   . 

4-454 
1.647 

'  -558 

.4308 

.000 

.     .     . 

1.838 
•431 

7-939 
1.862* 

1.845 

.4308 
.4308 

6.101 
M31* 

.558 

1.407 

6.077 

1.845 

.000 

4.670 

.558 

*Air  and  N,  equivalents  of  O3  in  wood. 

The  weight  of  air  theoretically  required  for  the  combustion 
of  one  pound  of  dry  wood  is  thus  6.077  pounds.  For  each  20 
per  cent  in  excess  of  this  weight  (i.  e.,  each  1.2154  pounds  of  air 
above  6.077),  there  will  appear  in  the  products  of  combustion. 

1.2154  x  .2315  — .2814  pounds  O2 
1.2154  x  .7685  — .9340  pounds  N2 

and  the  weight  of  the  products  of  combustion  per  pound  of  dry 
wood  for  varying  amounts  of  excess  air  will  be : 

TABLE    A 


Weight 
Products 
Perfect 
Combustion 

Weight  Products  —  Varying  Amounts  Excess  Air  —  Pounds 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

too  Per  Cent 

C02 
02 

N2 
H20 

1.845 
.OOO 
4.668 
.558 

1.845 
.281 

5.602 
.558 

1.845 

.563 
6.536 
.558 

1.845 
-844 
7.470 
.558 

1.845 
I.I26 

8.404 
.558 

1.845 
1.407 
9-338 

.558 

7.071 

8.286 

9.502 

10.717 

"•933 

I3-I48 

79 


Expressed  in  terms  of  percentage  weight,  these  values  are : 

TALBE   B 


Per  Cent 
Weight 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 
H2O 

26.093 
.000 
66.016 
7.891 

22.267 

3-391 
67.608 

6-734 

19.417 

5-925 
68.786 

5-872 

17.216 

7-875 
69.702 
5.207 

15.461 

9-436 

70.427 
4.676 

14.033 
10.701 
71.022 
4.244 

100.000 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

Expressed  in 
combustion  these 


terms  of  percentage  weight  of  dry  products  of 
values  are : 

TABLE   C 


Per  Cent 

Weight 
Dry  Products 
Perfect 
Combustion 

Per  Cent  Weight  Dry  Products—  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 

28.328 
.000 
71.672 

23.875 
3.636 

72.489 

20.628 
6.295 
73-077 

18.162 
8.307 

73-531 

16.219 

9.899 
73-882 

I4-655 
H.I75 
74.170 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

Converting  the  percentages  by  weight  into,  terms  of  per- 
centage by  volume  of  dry  products  of  combustion,  the  values  of 
Table  C  become : 


TABLE   D 


Per  Cent 
Volume 
Dry  Products 
Perfect 
Combustion 

Per  Cent  Volume  Dry  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 

20.097 
.OOO 
79-903 

16.721 

3-501 
79.778 

I4-3I3 
6.006 
79.681 

12.514 
7.870 
79.616 

II.II5 
9-327 
79-558 

9999 
10.483 

79-5'8 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

80 


In  order  to  compare  these  results  with  those  obtained  through 
the  use  of  the  combustion  formulae,  assume  that  the  wood  is 
burned  with  60  per  cent  excess  air  and  that  the  flue  gas  analysis 
shows  12.514  per  cent  CO2,  7.870  per  cent  O2,  and  79.616  per 
cent  N2. 

The  dry  gas  per  pound  of  carbon  from  formula  (27)  will  be 

ii  x  12.514+ 8x  7. 870+7  x  79.616 

—=20.189  pounds 
3x  12.514 

Since  the  wood  contains  no  sulphur,  no  correction  for  this 
constituent  is  necessary  to  the  carbon  weight,  and  the  weight  of 
dry  products  of  combustion  per  pound  of  dry  wood  is 

20. 189  x  .5031  =  10.157  pounds 
which  checks  with  the  value  of  Table  A,  viz. : 
10.717 — .558=10.159  pounds 

Since  for  each  pound  of  dry  wood  burned  there  are  .4610 
pounds  of  contained  moisture,  and  since  from  the  hydrogen  con- 
tent there  will  appear  in  the  flue  gases  .558  pounds  of  water 
vapor,  the  total  weight  of  products  per  pound  of  wood  will  be 

10.159+9  (.062)  +  .461  =  11. 1 78  pounds 

The  weight  of  dry  air  supplied  per  pound  of  carbon  from 
formula  (28)  is 

3.036  x  79.616 

—=19.316  pounds 
12.514 

and  the  dry  air  supplied  per  pound  of  wood 

19.316  x  .5031=9.718  pounds 

Since  the  nitrogen  content  of  the  wood  is  so  small  as  not  to 
appear  in  the  computations  of  the  products  of  combustion,  this 
value  will  check  with  the  weight  of  air  determined  from  Table  A 
and  the  ash  weight,  viz. : 

10.717 — (i. — .O04)=972i  pounds 

or  with  the  value  from  the  theoretical  amount  of  air  required  and 
60  per  cent  excess,  viz. : 

6.077+(.6x6.o77)=9.722  pounds 

If  we  accept  the  analysis  taken  as  typical  of  all  woods,  the 
approximate  weights  of  the  products  of  combustion  per  pound 

81 


Per  Cent  Excess  Air— Per  Cent 

20  40         60          80         ioo 


13  12          ii          10 

Products  of  Combustion  per  Pound  Dry  Wood -Pounds 


FIGURE  2 
WOOD.     CO2— Products  per  Pound  Dry  Wood. 


CO9 — Per  Cent  of  Excess  Air 


82 


of  dry  wood  corresponding  to  different  percentages  of  carbon 
dioxide,  and  the  amount  of  excess  air  which  such  weights  repre- 
sent, may  be  determined  graphically  from  Figure  2. 

OIL 

Given  an  oil  having  an  ultimate  analysis  as  follows: 

Per  Cent 

Carbon..     ,     .     .     ,     .     ....     .  84.00 

Hydrogen  .     ...     >     ...     .     .     .  12.70 

Oxygen .     .     .     .  1.20 

Sulphur       .     .     <: .  . '"..'. 0.40 

Nitrogen 1.70 


100.00 


With  perfect  combustion  the  oxygen  and  air  required  per 
pound  of  oil,  and  the  products  of  combustion  per  pound  will  be 
as  follows : 


Weight 
per  Pound 
Oil 
Pounds 

Required  —  Pounds 

Products  of  Combustion  —  Pounds  per  Pound  of  Oil 

02 

Air 

CO, 

02 

N2 

H20 

S02 

c 

H2 
02 

S 

N2 

.8400 
.1270 
.OI2O 
.0040 
.OI7O 

2.240 
1.016 

9.677 
4.389 

3.080 

,  '.   . 

7-437 
3-373 

I-I43 

.   .    . 

.0120 

.004 

.017 

.  ..  ... 

.013 
.017 

.     .     . 

.008 

O2  in  Oil 

3.260 
.012 

14.083 

.052* 

3.080 

.012 

.012 

10.840 
.040* 

I-  143 

.008 

SO2  as  CO2 

3.248 

14.031 

3.080 
.008 

.OOO 

10.800 

I-I43 

.008 
.008 

3.248 

14.031 

3.088 

.OOO 

10.800 

I-I43 

.000 

*Air  and  N2  equivalents  of  O2  in  oil. 

The  weight  of  air  theoretically  required  for  the  combustion 
of  one  pound  of  oil  is  then  14.031  pounds.  For  each  20  per 
cent  supplied  in  excess  of  this  weight  of  air  (i.  e.,  each  2.8062 


pounds   above    14.031),   there  will  appear  in  the  products  of 

combustion 

2.8062  x  .2315—   .6496  pounds  of  O2 
2.8062  x  .7685  —  2.1566  pounds  of  N2 

and  for  varying  amounts  of  excess  air  the  weights  of  the  products 

of  combustion  per  pound  of  oil  will  be : 

TABLE  A 


Weight 
Products 
Perfect 
Combustion 

Weight  Products  —  Varying  Amounts  Excess  Air  —  Pounds 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

100  Per  Cent 

C02 
02 
N2 
H20 

3.088 
.000 

10.800 

1.143 

3.088 
.650 
12-957 
I.I43 

3.088 
1.299 

*5-«3 

1-143 

3.088 
1.949 
17.270 
1.143 

3.088 
2.598 
19.426 
I-I43 

3.088 
3.248 
21.583 
1.  143 

15-031 

17.838 

20.643 

23.450 

26.255 

29.062 

Expressed  in  terms  of  percentage  weight,  these  values  are  : 

TABLE  B 


Per  Cent 

Weight 

Per  Cent  Weight  Products  —  Varying  Amounts  Excess  Air 

Perfect 
Combustion 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

CO2 

20.544 

17.311 

H-959 

13.169 

11.762 

10.626 

02 

.000 

3-644 

6.293 

8.311 

9-895 

11.176 

N2 

71.852 

72.637 

73-211 

73.646 

73-990 

74265 

H2O 

7.604 

6.408 

5-537 

4.874 

4-353 

3-933 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

Expressed  in  terms  of  percentage  weight  of  dry  products  of 
combustion,  these  values  are : 


Per  Cent 
Weight  Dry 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Dry  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 

22.235 
.000 

77.765 

18.496 
3-894 
77.610 

I5-836 
6.662 

77.502 

13.844 
8-737 
77-4I9 

12.297 

10-345 
77-358 

11.061 

11.634 

77-305 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

84 


Converting  these  percentages  by  weight  of  the  dry  products 
of  combustion  into  terms  of  percentage  by  volume,  the  values  of 
Table  C  become: 

TABLE  D 


Per  Cent 
Volume 
Dry  Products 
Perfect 
Combustion 

Per  Cent  Volume  Dry  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

CO2 
02 

N2 

15-395 
.000 

84.605 

12.686 
3.672 
83.642 

10.788 
6.240 
82.972 

9-384 
8.144 
82.472 

8.304 
9.605 
82.091 

7.446 
10.769 
81.785 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

Assume,  for  the  purpose  of  comparing  the  data  thus  com- 
puted with  the  results  obtained  from  the  use  of  the  combustion 
formulae,  that  the  oil  is  burned  with  20  per  cent  excess  air  and 
that  the  flue  gas  analysis  shows  12.686  per  cent  CO2,  3.672 
per  cent  O2,  and  82.972  per  cent  N2. 

The  weight  of  dry  products  of  combustion  per  pound  of 
carbon  is,  from  formula  (27) 

n  x  12.686+  8  x  3.672  -f  7  x  83.642 

'  ^  —  =  19.823  pounds 

3  x  12.686 

Multiplying  this  value  by  the  weight  of  carbon  per  pound  of 
oil  we  have  as  the  weight  of  dry  gas  per  pound  of  oil. 

19.823  x  .84=16.651  pounds 
as  against  the  value  from  Table  A 

17.838—1.143  =  16.695  pounds 

If  the  carbon  weight  is  corrected  for  the  sulphur  equivalent, 
the  two  values  may  be  made  to  check  exactly,  and  we  have  as 
the  weight  of  dry  gas  per  pound  of  oil 

19.823  x  [.84+  (.004-^1.833)]=  16.695  pounds 

The  total  gas  weight  per  pound  of  oil  will  be  the  dry  gas 
weight  plus  the  weight  of  moisture  resulting  from  the  burning 
of  .127  pounds  of  hydrogen,  or 

i6.695+(.i27  x  9)  =  17. 838  pounds 


10 


Per  Cent  Excess  Air— Per  Cent 
30          40  50          60  70 


80 


TOO 


30  28  26  24  2:2  20  1 8  16  14 

Products  of  Combustion  pet  Pound  of  Oil— Pounds 

FIGURE  3 
OIL.     CO 2 — Products  per  Pound  Oil.     CO2 — Per  Cent  of  Excess  Air 


86 


and  since  all  of  the  fuel  will  appear  in  the  products  of  combustion, 
the  weight  of  air  supplied  per  pound  of  oil  will  be 

17.838—1  —  16.838  pounds 

This  value  checks  with  the  computed  value  of  the  theoretical 
requirement  plus  20  per  cent  excess,  or 

14.031  +(.20  x  14.031)— 16.837  pounds 

The  weight  of  air  supplied  per  pound  of  carbon  from  formula 
(280)  is 

(3.036  x  83. 64) -f-i2. 686=20.01 7  pounds 

and  the  weight  per  pound  of  oil,  using  the  corrected  carbon  weight, 
20.017  x  [.84+ (.004 -5- 2.667)]  =  16.843  pounds 

the  slight  difference  between  this  value  and  the  actual  weight 
being  due  to  the  nitrogen  content  of  the  oil. 

If  the  analysis  of  oil  taken  be  accepted  as  typical  for  this 
class  of  fuel,  the  weight  of  the  products  of  combustion  per  pound 
of  oil  for  different  percentages  of  CO2,  and  the  per  cent  of  excess 
air  corresponding  to  such  CO2  may  be  determined  directly  from 
Figure  3. 

NATURAL  GAS 

Given  a  natural  gas  (Ohio)  having  an  analysis  by  volume 
as  follows: 

Per  Cent 

Carbon  Monoxide      .  .  . '   ..     .     .     .  0.45 

Hydrogen  .     .     .     .  .  .     ....  1.82 

Methane     .     .     .     »  .  .     ....  93.33" 

Ethylene     .     .     .     .  .  .     .     .     ,     .  0.25 

Hydrogen  Sulphide  .  .  *     .     .     .     .  0.18 

Oxygen       .     .     ,     .  ..:  .     ;r  .     .     .  0.35 

Carbon  Dioxide    .     .  .  .    V    .     .     .  0.22 

Nitrogen     .     .     ......     .     *••  3-4O 


100.00 

87 


Converting  this  analysis  by  volume  to  one  by  weight  we  have : 


Volume  per 
Cubic  Foot 

Weight  per 
Cubic  Foot 

Weight 
Pounds 

Per  Cent  by 
Weight 

CO 

.0045 

x 

.07806     = 

.OOO35I 

-          .046058         — 

0.762 

H2 

.0182 

x 

.00562     = 

.000102     - 

-          .O46O58          = 

0.221 

CH4 

•9333 

x 

.04500     = 

.041999     - 

-          .046058         = 

91.188 

C2H4 

.0025 

X 

.07808      = 

.OOOI95     - 

~          .046058          = 

0.423 

H2S 

.0018 

X 

.09600     = 

.OOOI73     ~ 

-          .046058          — 

0.376 

02 

.0035 

X 

.08921      = 

.O003I2 

-          .046058         = 

0.677 

C02 

.0022 

X 

.12341      = 

.OOO272     - 

-          .046058          = 

0.591 

N2 

.0340 

X 

.078O7      — 

.002654         -5-          .046058          = 

5762 

1  .0000 


.046058 


100.000 


The  weight  of  the  gas  is  thus,  under  standard  conditions, 
.046058  pounds  per  cubic  foot. 

With  perfect  combustion  the  oxygen  and  air  required  per 
pound  of  gas,  and  the  products  of  combustion  per  pound  will 
be  as  follows: 


Weight 
Per 
Pound 
Gas 
Pounds 

Required 
Pounds 

Products  of  Combustion  —  Pounds  Per  Pound  Gas 

02 

Air 

C02 

o, 

N2 

H20 

S02 

CO 
H2 
CH4 
C2H4 
H2S 
02 
N2 
C02 

.00762 
.OO22I 
.91188 
.00423 
.00376 
.00677 
•05762 
.00591 

.0044 
.0177 

3.6475 
.0145 

•0053 

.0188 
.0764 

15-7573 
.0626 
.0229 

.0120 

'*    '  •\- 

.0144 
.0587 

12.1098 
.0481 
.0176 

.0199 
2.0517 

•0055 
.0020 

.0071 

2.5077 

•OI33 

.    .    . 

.0068 

.0576 

.0059 

O2  in  Gas 

3.6894 
.0068 

15.9380 
.0294* 

2-5389 

.0068 
.0068 

12.3062 
.0226* 

2.0791 

.0071 

SO2as  CO2 

3.6826 

15.9086 

2-5389 
.0071 

.0000 

12.2836 

2.0791 

.0071 
.0071 

3.6826 

15.9086 

2.5460 

.0000 

12.2836 

2.0791 

.0000 

*Air  and  Na  equivalents  of  O2  present  in  gas. 

The  weight  of  air  theoretically  required  for  the  combustion 
of  one  pound  of  gas  is  thus  15.9086  pounds.     For  each  20  per 


cent  in  excess  of  this  weight  (i.e.,  each  3.1817  pounds),  there 

will  appear  in  the  products  of  combustion 

3.1817  x  .2315   =     .73656  pounds  O2 
3.1817  x  .7685  =   2.44513  pounds  N 2 

and  for   varying   amounts  .of   excess   air   the   weights   of   the 

products  of  combustion  per  pound  of  gas  will  be: 


Weight 
Products 
Perfect 
Combustion 

Weight  Products  Varying  Amounts  Excess  Air—  Pounds 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

100  Per  Cent 

C02 

02 

N2 
H20 

2.5460 
.0000 
12.2836 
2.0791 

2.5460 
.7366 
14.7287 
2.0791 

2.5460 
M731 
i7-T739 

2.0791 

2.5460 
2.2097 
19.6190 
2.0791 

2.5460 
2.9462 
22.0641 
2.0791 

2.5460 
3.6828 

24.S093 
2.0791 

16.9087 

20.0904 

23.2721 

26.4538 

29-6354 

32.8172 

Expressed  in  terms  of  percentage  weight  these  values  are : 

TABLE   B 


Per  Cent 
Weight 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Products—  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 

02 
N2 
H2O 

I5-057 
.OOO 
72.647 
12.296 

12.673 
3.666 
73-312 
10.349 

10.940 

6.330 
73.796 

8-934 

9.624 

8-353 
74.163 
7.860 

8.591 
9.942 
74-452 
7.015 

7-758 
11.222 
74.684 
6.336 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

Expressed  in  terms  of  percentage  weight  of  d  ry  products  of 
combustion  these  values  are : 

TABLE   C 


Per  Cent 
Weight 
Dry  Products 
Perfect 
Combustion 

Per  Cent  Weight  Dry  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 

17.168 
.000 
82.832 

14.136 
4.089 
81.775 

12.013 
6.951 
81.036 

10.445 
9.066 
80.489 

9-239 
10.692 
80.069 

8.283 
11.981 
79-736 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

89 


Converting  these  percentages  by  weight  of  the  dry  products 
of  combustion  into  terms  of  percentage  by  volume,  the  values  of 
Table  C  becomes : 

TABLE  D 


Per  Cent 
Volume 
Dry  Products 
Perfect 
Combustion 

Per  Cent  Volume  Dry  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

too  Per  Cent 

C02 

02 

N2 

11.652 
.000 
88.348 

9535 
3-792 
86.673 

8.067 
6.419 
85.5H 

6.991 

8-345 
84.664 

6.169 
9.8l7 
84.014 

5-520 
10.978 
83.502 

100.000 

100.000 

100.000 

100.000 

IOO.OOO 

IOO.OOO 

For  the  purpose  of  comparison  between  the  results  so  com- 
puted with  those  obtained  from  the  combustion  formulae,  assume 
that  the  gas  is  burned  with  40  per  cent  excess  air  and  the  flue 
gas  analysis  shows  8.067  Per  cent  CO2,  6.419  per  cent  O2,  and 
85.514  per  cent  N2. 

The  dry  gas  per  pound  of  carbon  from  formula  (27)  will  be : 

1 1  x  8.067+8  x  6.419+7  x  85.5 14 

3.  x  8.067  =30'5226  P°unds 

The  weight  of  carbon  per  pound  of  gas  will  be : 
From  CO       .00762  x  f  =.003266 
FromCH4    .9ii88x  f  =.683910 
From  C2H4  .00423  x  f  =.003626 
From  CO 2    .00591  x  ^=.001612 

Total  carbon     .692414  pounds 

Multiplying  the  weight  of  dry  gas  per  pound  of  carbon  by  this 
value,  we  have  as  the  dry  gas  per  pound  of  gas  burned 

30.5226  x  .6924=21.134  pounds 
while  the  value  from  Table  A  for  40  per  cent  excess  air  is 

23.2721—2.0791=21.193  pounds 

While  the  difference  in  these  values  is  negligible,  they 
may  be  made  to  check  still  more  closely  if  the  carbon  weight 
is  corrected  for  the  sulphur  equivalent.  The  weight  of  sulphur 
per  pound  of  gas  is 

.00376  x  H=.00354  pounds 


90 


The  weight  of  dry  gas  per  pound  of  gas  burned,  using  the 
corrected  carbon  weight  will  be,  then 

30.5226  x  [.69241 +  (.00354-^-1. 833X1=21.192  pounds 
The  weight  of  hydrogen  per  pound  of  gas  will  be 

From  H2  =.00221 

From  CH4  .QiiSSx  .1  =.22797 
From  C2H4  .00423  x  |  =.00060 
From  H2S  .00376  x  ^=.00023 

Total  H2      .23101  pounds 

while  the  weight  of  water  vapor  in  the  products  of  combustion 
per  pound  of  gas  from  this  hydrogen,  will  be 

.23101  x  9=2.0791  pounds 

The  total  gas  weight  per  pound  of  gas  burned  is  thus 
21.192  +  2.079=23.271  pounds 

With  gaseous  fuels,  since  the  total  weight  of  fuel  burned  will 
appear  in  the  products  of  combustion,  the  air  supplied  per  pound 
of  fuel  must  equal  the  total  products  per  pound  less  one,  or,  in 
the  present  instance,  the  air  supplied  per  pound  of  gas  will  be 

23.271  — 1  =  22.271  pounds 
which  checks  with  the  value  of  Table  A,  viz.: 

1 5. 9086+ (.40  x  I5.9o86)=22.272  pounds 

Since  all  gaseous  fuels  have  a  greater  or  lesser  nitrogen  content, 
this  method  for  the  computation  of  air  supplied  is  much  more 
accurate  .than  the  use  of  formula  (28)  and  is  also  simpler. 

The  heat  value  per  pound  of  this  natural  gas  may  be  com- 
puted from  the  analysis  by  weight  and  Table  6  as  follows : 

T  Weight  B.  t.  u.  T>    . 

Per  Pound        Per  Pound  I 

CO       .00762  x     4380  =        33 

H2  .00221    X    62000=         137 

CH4  .91188  x  23850  =  21748 
C3H4  .00423  x  21450=  91 
H2S  .00376  x  7458  =  28 

B.  t.  u.  per  pound  =  22037 
91 


Per  Cent  Excess  Air— Per  Cent 

20          40          60          80         100 


32  30  28  26  24  22  20  l8 

Products  of  Combustion  per  Pound  of  Gas  — Pounds 


FIGURE  4 

NATURAL  GAS.   CO2 — Products  per  Pound  Gas 
CO  2 — Per  Cent  Excess  Air 


92 


Since,  as  was  shown,  the  gas  under  standard  conditions 
weighs  .046058  pounds  per  cubic  foot,  the  heat  value  per  cubic 
foot  will  be 

22037  x  .046058=1015  B.  t.  u. 

To  illustrate  the  methods  of  computation  where  volumetric 
results  are  desired,  assume  the  same  natural  gas  analysis  as  given 
above.  The  volumes  of  oxygen  and  air  required  for  combustion 
and  the  volumetric  products  per  cubic  foot  of  gas  will  be  as 
follows : 


Volume 
PerCubic 
Foot  Gas 

Required  Cubic  Foot 

Products  of  Combustion—  Cubic  Feet 
Per  Cubic  Foot  Gas 

02 

Air 

C02 

02 

N2 

H20 

soa 

CO 
H2 
CH4 
C2H4 
H2S 
02 
C02 
N2 

.0045 
.0182 

•9333 

.0025 
.0018 

•0035 
.OO2I 
.0340 

.00225 
.OOQIO 
1.86660 
.00750 
.00270 

.01076 
•04352 
8.92608 

•03587 
.01291 

.0045 

.    .   . 

.0085 
•0344 
7-0595 

.0284 
.0102 

.0182 
1.8666 
.0050 
.0018 

.0018 

•9333 
.0050 

.    .    . 

•0035 

.0021 

.0340 

.   .    . 

O2  in  Gas 

1.88815 
.00350 

9.02914 

.01674* 

•9449 

•0035 
•0035 

7.1750 

.0132* 

1.8916 

.0018 

SO2  as  CO2 

1.88465 

9.01240 

•9449 
.0018 

.0000 

7.1618 

1.8916 

.0018 
.0018 

1.88465 

9.01240 

.9467 

.0000 

7.1618 

1.8916 

.0000 

*Air  and  N2  equivalents  of  O2  present  in  gas. 

N.  B. — It  is  of  interest  to  note  that  because  of  the  volumetric  relations  of  CO,  O3  and 
CO2,  H2,  O2  and  H2O,  and  H2S,  O2,  H2O  and  SO2,  the  total  volume  of  products  is  not 
equal  to  the  volume  of  the  gas  plus  the  volume  of  the  air  supplied. 

One  cubic  foot  of  gas  will  thus  require  9.0124  cubic  feet  of 
air  for  perfect  combustion.  If  we  assume,  as  in  the  computations 
on  a  weight  basis,  that  the  gas  is  burned  with  40  per  cent  excess 
air,  there  will  appear  in  the  products  of  combustion  in  addition  to 
the  volumes  given  above 

9.0124  x  .40  x  .2091=   .7538  cubic  feet  O2 
9.0124  x  .40  x  .7909=2.8512  cubic  feet  N2 


93 


For  40  per  cent  excess  air  then,  the  volumes  of  the  products 
of  combustion,  these  volumes  expressed  in  terms  of  percentage 
volume,  and  expressed  in  terms  of  percentage  volume  of  dry 
products  will  be 

Volume  Products  Per  Cent  Volume  Per  Cent  Volume 

per  Cubic  Foot  Products  Dry  Products 

CO2                   .9467  6.958  8.082 

O2                    .7538  5.541  6.432 

N2                 10.0130  73-597  85.514 

H2O                 1.8916  13-904  .  .  . 

13.6051  100.000  100.000 

The  dry  gas  analysis  as  thus  computed  on  a  direct  volumetric 
basis  may  be  considered  to  check  the  analysis  computed  on 
the  basis  of  weight,  the  maximum  difference  being  0.26  per  cent. 
The  slight  difference  is  due  to  the  fact  that  the  weights  of 
oxygen  required  per  pound  of  the  various  combustible  substances 
as  given  in  Table  8  do  not  exactly  check  with  the  correspond- 
ing volumes  of  oxygen  required  as  given  in  Table  9.  The 
variation  between  these  sets  of  corresponding  values  results 
from  the  use  of  the  approximate  instead  of  the  accurate  atomic 
and  molecular  weights  in  the  computation  of  the  proportionate 
parts  by  weight  of  the  constituents  of  the  combustible  substances 
in  Table  8.  Any  error  arising  from  this  source  may  be  neglected. 

The  heat  value  per  cubic  foot  of  this  natural  gas  may  be 
computed  from  the  analysis  by  volume  and  Table  6  as  follows  : 

.  T       Volume  per          B.  t.  u.  per  -r,   «. 

Cubic  Foot        Cubic  Foot  I 

CO     .0045  x     341.9—         1.5 

H2      .0182  x     348.4  =        6.3 

CH4    -9333  x  1073.2  —  1001.6 

C2H4  .0025  x  1674.8  —        4.2 

H2S    .0018  x     716.0—         1.3 

B.  t.  u.  per  cubic  foot  1014.9 

This  value  checks  with  the  value  already  computed  from  the 
analysis  by  weight. 

If  we  accept  the  analysis  taken  as  typical  of  natural  gas,  the 
approximate  weights  of  the  products  of  combustion  per  pound  of 
gas  burned,  and  the  percentage  of  excess  air,  corresponding  to 
different  percentages  of  CO2,  for  this  class  of  fuel,  may  be 
determined  directly  from  Figure  4. 

94 


BY-PRODUCT  COKE  OVEN  GAS 

Given  a  by-product  coke  oven  gas  having  an  analysis  by 
volume  as  follows : 

Per  Cent 


Carbon  Dioxide  . 
Carbon  Monoxide 
Methane  .J  ,  , 
Hydrogen  .  .  . 


0.75 

6.00 

28.15 

53.00 


Nitrogen 12.10 


100.00 


Converting  the  analysis  by  volume  to  one  by  weight,  we  have : 


Volume  per 
Cubic  Foot 


Weight  per 
Cubic  Foot 


Weight 
Pounds 


Per  Cent 
Weight 


CO, 
CO 


H 

N. 


.0075 

X 

.12341 

—  .00093 

-j- 

.03071  = 

3.03 

.0600 

X 

.07806 

=  .00468 

-f- 

.03071  == 

15.24 

.2815 

X 

.04500 

=   .01267 

-f- 

.03071  = 

41.26 

.5300 

X 

.OO562 

=  .O0298 

•4- 

.03071  = 

9.70 

.I2IO 

X 

.07807 

=  .00945 

-i- 

.03071  = 

30-77 

1 .0000 


100.00 


.03071 

The  weight  of  the  gas  is  thus,  under  standard  conditions, 
.03071  pounds  per  cubic  foot. 

With  perfect  combustion,  the  oxygen  and  air  required  per 
pound  of  gas,  and  the  products  of  combustion  per  pound  will  be 
as  follows : 


Weight 
per  Pound 

Pounds 

Required  per  Pound  Gas 
Pounds 

Products  of  Combustion  per  Pound  Gas 

02 

Air 

C02 

N9 

H20 

C02 
CO 
CH4 
H2 

N2 

.0303 
.1524 
.4126 
.0970 

•3°77 

.030 
•239 

.087 
1.651 
.776 

•375 
7-132 
3-352 

.288 
5.481 
2.576 
.308 

.929 

-873 

I  .OOOO 

2.514 

10.859 

1.404 

8.653 

1.  802 

The  weight  of  air  theoretically  required  for  the  combustion 
of  one  pound  of  gas  is  thus  10.859  pounds.    For  each  20  per 


95 


cent  in  excess  of  this  amount  (i.  e.y  each  2.172  pounds  above 

10.859)  there  will  appear  in  the  products  of  combustion 
2.172  x  .2315—   .503  pounds  O2 
2.172  x  .7685—1.669  pounds  N2 

and  for  varying  amounts  of  excess  air  the  weights  of  the  products 

of  combustion  per  pound  of  gas  will  be: 

TABLE  A 


Weight 

Weight  Products  —  Varying  Amounts  of  Excess  Air  —  Pounds 

Products 

Perfect 

Combustion 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

100  Per  Cent 

C02 

1.404 

1.404 

1.404 

1.404 

1.404 

1.404 

02 

.000 

•503 

1.  006 

1.509 

2.OI2 

2.515 

N3 

8.653 

10.322 

11.991 

13.660 

I5-329 

I6.998 

H20 

1.802 

1.  802 

1.  802 

1.  802 

1.  802 

1.  802 

11.859 

14.031 

16.203 

18.375 

20-547 

22.719 

Expressed  in  terms  of  percentage  weight  these  values  are: 

TABLE  B 


Per  Cent 
Weight 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Products  —  Varying  Amounts  of  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

too  Per  Cent 

C02 

02 
N2 
H20 

11.839 
.000 
72.966 
I5-I95 

IO.OO7 
3-585 
73-565 
12.843 

8.665 
6.209 
74.005 
II.  121 

7.641 
8.212 
74-340 
9.807 

6-833 
9-792 
74.605 
8.770 

6.180 

11.070 
74.818 
7-932 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

Expressed  in 
combustion  these 


terms  of  percentage  weight  of  dry  products  of 
values  are  : 

TABLE  C 


Per  Cent 
Weight  Dry 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Dry  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

too  Per  Cent 

C02 
02 

N2 

13.960 
.000 

86.040 

11.482 

4."3 

84.405 

9-749 
6.986 
83.265 

8.472 
9.105 
82.423 

7.490 
10-733 
81.777 

6.712 
12.024 
81.264 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

96 


Converting  these  percentages  by  weight  of  the  dry  products 
of  combustion  into  terms  of  percentage  by  volume,  the  values  of 
Table  C  become : 

TABLE  D 


Per  Cent 
Volume  Dry 
Products 
Perfect 
Combustion 

Per  Cent  Volume  Dry  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 

9-359 

.000 

90.641 

7-666 
3-776 
88.558 

6.491 
6.396 
87.113 

5.629 
8.318 
86.053 

4.968 
9.789 
85.243 

4447 

^0-953 
84.600 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

For  the  purpose  of  comparing  the  results  so  computed  with 
those  obtained  from  the  combustion  formulae,  assume  that  the 
gas  is  burned  with  40  per  cent  excess  air  and  that  the  flue  gas 
analysis  shows  6.491  per  cent  CO2,  6.396  per  cent  O2,  and 
87.113  per  cent  Na. 

The  weight  of  dry  gas  per  pound  of  carbon  from  formula 
(27)  will  be 

1 1  x  6.49 1  +  8  x  6.396  +7x87.113 

3x6.491  =37.609  pounds 

The  weight  of  carbon  per  pound  of  gas  burned  is 

From  CO2  .0303  x  T3T  =  .0083 
From  CO  .1524  x  f  =  .0653 
From  CH4  .4126  x  f  —  .3094 

Total  carbon  =  .3830  pounds 
and  the  weight  of  dry  products  per  pound  of  gas 
37.609  x  .3830=14.404  pounds 
The  weight  of  hydrogen  per  pound  of  gas  burned  is 

From  H2  —.0970 

From  CH4  .4126  x  £=.1032 

Total  H2     .2002  pounds 

and  the  weight  of  water  vapor  formed  in  the  burning  of  this 
hydrogen  will  be 

.2002  x  9=1.802  pounds 


97 


Per  Cent  Excess  Air— -Per  Cent 
20          40         60          80 


100 


O 


22  20  l8  l6  14  12 

Products  of  Combustion  per  Pound  Gas  — Pounds 

FIGURE  5 

BY-PRODUCT  COKE  OVEN  GAS.    CO 2— Products  per  Pound  Gas 
CO*—  Per  Cent  Excess  Air 


98 


The  total  weight  of  the  products  of  combustion  per  pound  of 
gas  burned  will  thus  be 

14.404  +  1.802=16.206  pounds 

which  value  checks  with  the  computed  value  of  Table  A  for  40 
per  cent  excess  air. 

Since  all  of  the  gas  appears  in  the  products  of  combustion, 
the  weight  of  air  supplied  per  pound  of  gas  burned  is 

1 6.206— 1  =  15 .206  pounds 

which  checks  with  the  value  computed  from  the  weight  of  air 
theoretically  required  and  40  per  cent  excess  air,  viz. : 
10. 859 +  (.40  x  10. 859)  =  1 5. 203  pounds 
The   weight   of   air   supplied    per   pound   of   carbon   from 
formula  (28)  is  6x8 

6.491          =40'78  P°unds 
and  the  weight  of  air  per  pound  of  gas 

40.78  x  .3830=15.619  pounds 

The  error  resulting  from  the  use  of  formula  (28)  for  this 
particular  gas  is  2.7  per  cent.  In  view  of  the  nitrogen  content  of 
the  gas  (12.1  per  cent  by  volume  and  30.77  per  cent  by  weight) 
this  error  appears  smaller  than  might  be  expected,  but  this  is 
due  to  the  fact  that  while  the  nitrogen  content  is  high,  the  total 
nitrogen  per  pound  of  gas  is  small  as  compared  with  the  amount 
of  nitrogen  in  the  air  required  for  combustion. 

The  heat  value  per  pound  of  this  gas  may  be  computed  from 
the  analysis  by  weight  and  Table  6  as  follows : 

T          Weight  per       B.  t.  u.  per  „ 

Pound  Pound  I 

CO      .1524  x     4380  =      667.5 

CH4     .4126  x  23850  =    9840.5 

H2       .0970  x  62000  =    6014.0 

B.  t.  u.  per  pound  =  16522.0 

and    since,  under  standard    conditions,  the  gas  weighs  .03071 
pounds  per  cubic  foot,  the  heat  value  per  cubic  foot  will  be 

.03071  x  16522=507.3  B.  t.  u. 

If  we  accept  the  analysis  taken  as  typical  of  by-product  coke 
oven  gas,  the  weights  of  the  products  of  combustion  per  pound 
of  gas  burned,  and  the  percentage  of  excess  air,  corresponding 
to  different  percentages  of  carbon  dioxide,  may  be  determined 
directly  from  Figure  5 

99 


BLAST  FURNACE  GAS 

Given  a  blast  furnace  gas  having  an  analysis  by  volume,  dry,* 
as  follows: 

Per  Cent 

Carbon  Dioxide 12.50 

Carbon  Monoxide 25.40 

Hydrogen  .     ,s  .     .     .     ,     ^  •..:..       3.50 
Nitrogen     .     .     ..:...     .     *     .     58.60 
Converting  the  analysis  by  volume  to  one  by  weight,  we  have: 


Volume  per 
Cubic  Foot 


Weight  per 
Cubic  Foot 


Weight 
Pounds 


Weight 
Per  Cent 


CO2 

.1250 

X 

.12341  = 

•01543 

•H- 

.08121 

—   IQ.OOO 

CO 

.2540 

X 

.07806  = 

.01983 

-=- 

.08121 

=  24.418 

H2 

.0350 

X 

.00562  = 

.00020 

4- 

.08  1  2  I 

.246 

N2 

.5860 

X 

.07807  = 

.04575 

-7- 

.08121 

==  56.336 

i.oooo  .08121  100.000 

The  weight  of  the  gas  is  thus,  under  standard  conditions, 

.08121  pounds  per  cubic  foot. 

With  perfect  combustion  the  oxygen  and  air  required  per 

pound  of  gas,  and  the  products  of  combustion  per  pound,  will  be 

as  follows : 


Weight 
Per 

Required  per  Pound  Gas  — 
Pounds 

Products  of  Combustion  per  Pound  Gas 

Gas 
Pounds 

02 

Air 

C02 

N2 

HaO 

CO, 

IQOOO 

IQOO 

CO 

.24418 

.1392 

.6007 

•3834 

.4615 

H2 

.00246 

.0197 

.0850 

.      ••'•.' 

•0653 

.0221 

N2 

•56336 

.     .     . 

-      •      • 

.      .      . 

•5634 

-;  •     •' 

.1589 

•6857 

•5734 

1  .0902 

.0221 

The  weight  of  air  theoretically  required  for  the  combustion 
of  one  pound  of  gas  is  thus  .6857  pounds.  For  each  20  per  cent 
in  excess  of  this  amount  (i.  e.t  each  .13714  pounds  above  .6857) 
there  will  appear  in  the  products  of  combustion 

.13714  x  .23i5  =  .O3i75  pounds  O2 
.13714  x  .7685  =  . 10539  pounds  N2 

*While  blast  furnace  gas  contains  a  considerable  amount  of  moisture,  varying  with  the 
water  in  the  charge  and  the  amount  used  for  dampening,  it  is  customary  to  give  the  analysis 
on  a  dry  basis,  reporting  the  moisture  separately  in  terms  of  grains  per  cubic  foot  of  gas. 
The  moisture  content  is  ordinarily  about  30  or  35  grains  per  cubic  foot. 


100 


and  for  varying  amounts  of  excess  air  the  weights  of  the  products 
of  combustion  per  pound  of  gas  will  be : 


TABLE   A 


Weight 

Weight  Products  —  Varying  Amounts  of  Excess  Air  —  Pounds 

Products 

Perfect 

Combustion 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

too  Per  Cent 

C02 

•5734 

•5734 

•5734 

•5734 

•5734 

•5734 

°2 

.0000 

.0318 

•0635 

•0953 

.1270 

.1588 

N2 

1.0902 

1.1956 

1.3010 

1  .4064 

1.5118 

1.6172 

H20 

.0221 

.O22I 

.0221 

.O22I 

.O22I 

.0221 

1.6857 

1.8229 

i  .9600 

2.0972 

2-2343 

2-3715 

Expressed  in  terms  of  percentage  weight,  these  values  are: 

TABLE   B 


Per  Cent 
Weight 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Products—  Varying  Amounts  of  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

CO2 
02 
N2 
H2O 

34.016 
.OOO 
64.673 
I.3H 

3M55 

1-745 
65.588 

1.  212 

29.255 
3.240 
66.377 
I.I28 

27-34I 

4-544 
67.061 
1.054 

25.664 
5-684 
67.663 
.989 

24.179 
6.696 
68.193 
-932 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

Expressed  in  terms  of  percentage  weight  of  dry  products  of 
combustion,  these  values  are : 


TABLE  c 


Per  Cent 
Weight  Dry 
Products 
Perfect 
Combustion 

Per  Cent  Weight  Dry  Products  —  Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 

34.468 
.OOO 
65-532 

31.841 
1.766 
66.393 

29.589 
3-277 
67-I34 

27.632 

4-593 

67-775 

25.920 
5-741 
68-339 

24.406 

6-759 
68.835 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

101 


Per  Cent  Excess  Air— Per  Cent 
20  40  60          80          100 


!•••*"••! 


2.4  2.3  2.2  2.1  2.0  1.9  1.8  1-7 

Products  of  Combustion  per  Pound  Dry  Gas— Pounds 

FIGURE  6 

BLAST  FURNACE  GAS.     CO2 — Products  per  Pound  Gas 

CO2— Per  Cent  Excess  Air 

102 


Converting  these  percentages  by  weight  of  the  dry  products 
of  combustion  into  terms  of  percentage  by  volume,  the  values  of 
Table  C  become : 

TABLE   D 


Per  Cent 
Volume  Dry 
Products 
Perfect 
Combustion 

Per  Cent  Volume  Dry  Products  —Varying  Amounts  Excess  Air 

20  Per  Cent 

40  Per  Cent 

60  Per  Cent 

80  Per  Cent 

ioo  Per  Cent 

C02 
02 

N2 

25.077 
.000 
74-923 

22.973 
I-752 

75-275 

21.197 
3.228 

75-575 

19.674 
4.496 
75-830 

18-357 
5-590 
76-053 

17.203 

6-551 
76.246 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

IOO.OOO 

For  the  purpose  of  comparing  the  results  so  computed  with 
those  obtained  from  the  combustion  formulae,  assume  that  the 
gas  is  burned  with  40  per  cent  excess  air,  and  that  the  flue  gas 
analysis  shows  21.197  Per  cent  CO2,  3-228  per  cent  O2,  and 
75-575  percent  N9. 

The  weight  of  dry  gas  per  pound  of  carbon  will  be  from 
formula  (27) 

n  x  21.197+8  x  3.228  +  7  x  75.575 

^-±==12.392  pounds 
3  x  21.197 

The  weight  of  carbon  per  pound  of  gas  burned  is 

From  CO2  .19900  x  T3T  =  .0518 
From  CO    .24418  x  ^   —  .1046 

Total  carbon  =  .1564  pounds 

and  the  weight  of  dry  products  per  pound  of  gas 
12.392  x  .1564=1.938  pounds 

The  weight  of  water  vapor  formed  in  the  burning  of  the 
hydrogen  content  of  the  gas  will  be,  per  pound  of  gas 

9  x  .00246=. 022 1  pounds 

and  the  total  weight  of  the  products  of  combustion  per  pound 
of  dry  gas 

1.9 3 8  +.02 2  =1.960  pounds 

which  value  checks  with  the  computed  value  of  Table  A. 


103 


Since  all  of  the  gas  appears  in  the  products  of  combustion, 
the  weight  of  air  supplied  per  pound  of  dry  gas  burned  must  be 

1.960 — i. =.960  pounds 

which  checks  with  the  value  computed  from  the  weight  of  air 
theoretically  required  and  40  per  cent  excess  air  viz.: 
.68 5 7+ (.40  x  .68  5  7)  =  .960  pounds 

Blast  furnace  gas  offers  the  best  example  of  the  unsuitability 
of  formula  (28}  for  application  in '  the  case  of  all  fuels,  for  not 
only  is  the  nitrogen  content  high  (over  50  per  cent),  but  it  is 
large  in  proportion  to  the  total  nitrogen  in  the  products  of 
combustion,  even  with  great  amounts  of  excess  air. 

If,  for  the  present  example,  we  apply  this  formula,  the  weight 
of  air  supplied  per  pound  of  carbon  will  be 

3.036x75.575^ 

21.197 
and  the  weight  of  air  supplied  per  pound  of  gas 

10.824  x  .1564—1.693  pounds 

As  compared  with  the  correct  weight  (.960  pounds)  formula  (28) 
results  in  an  error  of  76.3  per  cent,  and  the  error  would  be  still 
greater  were  the  gas  burned  with  less  than  40  per  cent  excess  air. 
The  heat  value  per  pound  of  the  blast  furnace  gas,  from  the 
analysis  by  weight  and  Table  6,  is 

CO    . 24418  x    4380=1069.5 
H2    .00246x62000=   152.5 

I222.O  B.  t.  U. 

Since, the  gas,  under  standard  conditions,  weighs  as  shown, 
.08121  pounds  per  cubic  foot,  the  heat  value  per  cubic  foot  is 

.08121  x  1222=99.2  B.  t.  u. 

Or,  the  heat  value  per  cubic  foot,  from  the  volumetric  analysis 
and  Table  6,  is  CQ    .254x  342=86.9 

H2    .035x348=12.2 

99.1  B.  t.  u. 

If  we  accept  the  analysis  of  blast  furnace  gas  taken  as  typical 
of  this  fuel  as  a  class,  the  approximate  weights  of  the  products  of 
combustion  per  pound  of  dry  gas  burned,  and  the  percentages 
of  excess  air,  corresponding  to  various  percentages  of  carbon 
dioxide,  may  be  determined  directly  from  Figure  6. 

104 


HEAT  BALANCE 

A  in  the  case  of  the  combustion  data  just  discussed,  the 
computations  involved  in  the  determination  of  the  distri- 
bution of  losses  in  a  boiler  test,  i.  e.t  the  "heat  balance," 
are  best  illustrated  by  example. 

SOLID  OR  LIQUID  FUELS 

Where  the  weight  of  fuel  burned  can  be  actually  weighed, 
(e.  g.,  coal,  oil,  or  wood)  or  accurately  measured  (e.  g.,  natural  gas), 
the  computations  are  direct.  The  radiation  loss  and  the  small 
losses  which  cannot  be  computed  from  ordinary  test  data  are,  as 
stated,  grouped,  and  are  taken  as  the  difference  between  100  per 
cent  and  the  sum  of  the  known  and  distributable  losses. 

As  an  example  of  this  class  of  heat  balance,  let  us  consider 
one  of  the  tests*  at  the  plant  of  the  Detroit  Edison  Company, 
in  which  the  test  data  and  calculated  results  necessary  for  the 
computation  of  the  heat  balance  were  as  follows : 

Wet  Bulb  Thermometer,  Degrees  Fahrenheit  ....  67 

Temperature  Boiler  Room,  Degrees  Fahrenheit     ...  73 

Temperature  Exit  Gases,  Degrees  Fahrenheit  .     .     .     ..  575 

f  C,  Per  Cent 78.42 

H2,  Per  Cent     .....'.....  5.56 

O2,  Per  Cent     .     .     .     .     .     .     .     .     .     .  8.25 

N2,  Per  Cent     .     .     .     .     ...     .     .     .  1.09 

S,  Per  Cent i  .00 

Ash,  Per  Cent  .    ...    .     .     .     .     .-    .'     .     .  5.68 

Moisture  in  Coal,  Per  Cent  ....     .     .     .  ,  .     .     .     .  1.91 

B.  t.  u.  per  Pound  Dry  Coal  .     .     .     ....     .     .     .     .  14000 

Ash  and  Refuse  (Per  Cent  Dry  Coal)      :'•/  •'.-,•     -     •  7-°3 

Unconsumed  Carbon  in  Ash,  Per  Cent    .     .     .     .     ^     .  31.50 

(CO2,  PerCent.     .     .     .     .     .     .     .     .     .  14.00 

O2,  Per  Cent    .     .     .     ;     .     .     ....     .  5.50 

CO,  PerCent    .     .     .     .     .     .     .     .     .     ,  0.42 

N2,  Per  Cent    ,     .     .     .   '.     .     .     .     .     .  80.08 

Evaporation    from    and    at    212    Degrees    per    Pound 

Dry  Coal,  Pounds     .     *     .     ,     .     .     .     .     -     .     .  11.12 

* "  Tests  of  Large  Boilers  at  the  Detroit  Edison  Company."— D.  S.  Jacobus,  Trans. 
A.  S.  M.  E.— Volume  33. 

105 


Ultimate 
Analysis    « 
Dry  Coal 


Heat  Absorbed  by  Boiler 
The  heat  absorbed  by  the  boiler  per  pound  of  dry  coal  is 

ii. 12  x  970.4=10791  B.  t.  u. 
and  the  efficiency  of  the  boiler 

10791-^-14000=77.08  per  cent 

Loss  Due  to  Moisture  in  Coal 

The  moisture  in  the  coal,  1.91  per  cent,  becomes  in  terms  of 

dry  coal 

1.91-^(100 — i. 91)= i. 95  per  cent 

and  the  loss  due  to  this  moisture  content  is 

.0195  [(212—73)  +  970.4+48  (575— 2i2)]=25  B.t.u. 

25-^-14000=0.18  per  cent 

Loss  Due  to  the  Burning  of  Hydrogen 
This  loss  per  pound  of  dry  coal  is 
.0556x9. [(212— 73)4-970.4+ .48  (575—212)1=642  B.  t.  u. 

or 

642-^14000=4.58  per  cent 

Loss  Due  to  Heat  in  Dry  Chimney  Gas 
The  weight  of  dry  gas  per  pound  of  carbon  from  formula  (27}  is 
ii  x  14.00+8  x  5.50+7  (.42+80.08) 
3  (14.00+42) 

The  weight  of  carbon  per  pound  of  dry  fuel  is  .7842  pounds. 
Certain  of  this  carbon,  however,  is  not  burned,  as  evidenced  by 
the  unconsumed  carbon  in  the  ash.  Expressed  in  terms  of  total 
carbon,  the  unburned  weight  is 

.0703  x  .3 1 5 =.0221  pounds 

and  the  weight  of  carbon  burned  per  pound  of  dry  coal,  and 
passing  off  with  the  chimney  gases  is 

.7842 — .0221  =  7621  pounds 
1 06 


This  carbon  weight  must  be  further  corrected  for  the  sulphur 
equivalent  as  previously  explained,  and  applying  such  correction, 
the  weight  of  dry  gas  per  pound  of  dry  coal  becomes 

01 
17.603  x  (.7621  +          )=!  3-41  2  pounds 


The  loss  then,  due  to  heat  carried  away  in  the  dry  chimney 
gases  per  pound  of  dry  coal  is 

13.412  x  .24  x  (575  —  73)=i6i6  B.  t.  u. 
or 

i6i6-j-  14000—  11.54  per  cent 

Loss  Due  to  Moisture  in  Air 

From  the  wet  and  dry  bulb  thermometer  readings  and 
psychrometric  tables  the  weight  of  moisture  in  the  air  per  pound 
of  dry  air  supplied  is  .0127  pounds. 

The  weight  of  dry  air  supplied  per  pound  of  dry  coal  from 
formula  (28)  is,  using  as  the  carbon  weight*  that  which  is  burned 
and  passes  up  the  stack. 

3.036  x  80.08 
14.00+42    X  (•7842—  .0221)*==  12.849  pounds 

The  weight  of  water  vapor  per  pound  of  dry  coal  is 

12.849  x  .0127=.  163 
The  loss  due  to  the  moisture  in  the  air  is  then 

.163  x  .48  (575  —  73)^39-3  B.  t.  u. 
or 

39.3-^14000—0.28  per  cent 

Loss  Due  to  Incomplete  Combustion  of  Carbon 

This  loss,  from  formula  (34),  using  the  carbon  weight  actually 
burned  and  passing  up  the  stack,  and,  as  in  the  case  of  dry  chimney 
gas  loss,  corrected  for  the  sulphur  equivalent,  is 

0.42  .01 

x(762iH  —  3  —  )x  10160=226.6  B.  t.  u. 


14.00+0.42  '  1.833 

or 

226.6-^-14000—1.62  per  cent 

*The  total  loss  due  to  the  moisture  in  the  air  is  so  small  that  there  is  no  necessity  of 
correcting  the  carbon  weight  for  the  sulphur  equivalent.  In  the  present  case  such  a 
correction  would  not  affect  the  result. 

107 


Loss  Due  to  Carbon  in  the  Ash 
This  loss  from  formula  (J5)  is 

•°7°3*3i.5  x  14600=323.3  B.  t.  u. 

I OO 

or 

323.3-^-14000=2.31  percent 

Radiation  and  Unaccounted  Losses 
The  radiation  and  unaccounted  losses  will  be 
14000—  (10791  +  25  +  642+  1616+39+  227+  323)^337  B.t.u. 

or 

337-^-14000  =  2.41  percent 

The  complete  heat  balance  is  then 

B.  t.  u.  Per  Cent 

Heat  absorbed  by  boiler     ......     .    •    10791  77.08 

Loss  due  to  moisture  in  coal  ......  25  0.18 

Loss  due  to  moisture  formed  in  burning.  H2  .  642  4.58 

Loss  in  dry  chimney  gases      ......  1616  H-54 

Loss  due  to  moisture  in  air     .     .     .     .     .     .  39  0.28 

Loss  due  to  incomplete  combustion  of  C  .    '.."  227  1.62 

Loss  due  to  unconsumed  C  in  ash    .     .     .     .  323  2.31 

Radiation  and  unaccounted  losses     ....  337  2.41 

14000     100.00 

It  is  of  interest  to  note  that  the  radiation  and  unaccounted 
losses  for  the  test  considered  are  as  low  as  2.41  per  cent. 
Generally  speaking,  these  losses  are  one  of  the  best  indications 
of  the  accuracy  of  a  boiler  test,  and  where  a  heat  balance  shows 
an  excessive  unaccounted  loss  it  is  well  to  scrutinize  the  test 
data  most  carefully  before  accepting  the  results  without  question. 

GASEOUS  FUELS 

With  certain  gaseous  fuels  it  is  impossible  accurately  to 
measure  the  amount  of  fuel  burned  without  resorting  to  methods 
of  metering  which  are  not  available  in  most  tests.  In  such 
cases  the  heat  absorbed  by  the  boiler  per  unit  of  fuel  burned, 
and  therefore  the  efficiency  of  the  boiler,  cannot  be  directly 
determined.  Since,  however,  all  of  the  combustion  losses,  except, 

108 


of  course,  the  radiation  and  unaccounted  loss,  can  be  computed 
directly,  a  heat  balance  not  only  indicates  the  distribution  of 
losses,  but  offers  a  means  of  indirectly  determining  the  boiler 
efficiency.  For  such  determination  it  is  necessary  to  assume 
the  radiation  and  unaccounted  loss,  but  experience  has  fixed  the 
amount  of  such  loss  within  reasonably  accurate  limits. 

Blast  furnace  gas  is  the  fuel  in  most  common  use  that  cannot 
readily  be  measured,  and  we  will  consider  a  test  with  this  gas  in 
which  the  data  necessary  for  the  computation  of  a  heat  balance 
are  as  follows  : 

Temperature  Boiler  Room,  Degrees 60 

Temperature  Exit  Gases,  Degrees 550 

.      .     .    _          fC02,  PerCent 13.0 

Analysis  Dry          ~~ a  _      „  ., 

_      *  y          CO,  Per  Cent 25.6 

Gas  by  Volume^   TT     „      _ 

.f   V<  H9,  Per  Cent 3.2 

at  60  Degrees  *'          ~ 

(^  N2,  Per  Cent 58.2 

Moisture  in  Gas  (Grains  per  Cubic  Foot),  Grains  ...  32 

Temperature  Gas  Entering  Burner  Degrees 300 

(  CO2,  Per  Cent 21.2 

Flue  Gas  J  O2,  Per  Cent 3.7 

Analysis  j  CO,  Per  Cent 0.6 

L  N2,  Per  Cent ,,     .  74-5 

We  will  assume  that  the  radiation  and  unaccounted  loss, 
including  the  loss  due  to  the  moisture  in  the  air  supplied  for 
combustion  is  5.0  per  cent. 

It  would,  of  course,  be  possible  to  compute  the  heat  balance 
either  on  a  volumetric  or  on  a  weight  basis,  but  since  the  common 
combustion  formulae  are  in  terms  of  weight  the  latter  basis 
appears  preferable. 

Converting  the  analysis  of  the  gas  by  volume  to  one  by 
weight,  we  have 

Volume  per  Weight  per  Weight  Weight 

Cubic  Foot  Cubic  Foot  Pounds  Per  Cent 

CO2  .130  x  .12341  =  .01604  -*-  .08164  =  19.647 
CO  .256  x  .07806  =  .01998  -*-  .08164  =  24.473 

H2   .032   X   .00562   =   .00018   -5-   .08164   —      .221 

N2   .582  x  .07807  —  .04544  -T-   .08164  —   55-^59 

.08164  100.000 

109 


The  weight  of  the  gas  then  at  60  degrees  is  .08164  pounds 
per  cubic  foot. 

The  heat  of  the  gas  will  be  value 

.24473  x    438o  =  1071.9 

.00221   X  62000  —      137.0 

B.  t.  u.  per  pound  =  1208.9 
or  at  60  degrees 

1208.9  x  .08164—98.7  B.  t.  u.  per  cubic  foot. 

Since  the  gas  enters  the  boiler  at  a  temperature  above  that 
of  the  atmosphere,  there  is  available  in  the  gas  for  absorption  by 
the  boiler  a  definite  amount  of  sensible  heat  aside  from  the  heat 
developed  by  the  combustion  of  the  gas,  and  the  heat  balance 
therefore  must  be  computed  on  the  basis  of  above  atmospheric 
temperature. 

This  sensible  heat  per  pound  of  gas  will  be 

c  (T->) 

where  £=mean  specific  heat  of  gas, 

T—  temperature  entering  gas, 
/—  temperature  atmosphere. 

The  mean  specific  heat  of  the  gas  between  60  degrees  and 
300  degrees  is 
CO2  =  .  1965  (.1983  +  .  000042  x  360  —  .0000000056  x  111600) 

=  .0418 

CO  =.2447(.2343  +  .ooooios  x  360)  =.0583 

.000266x360)  =.0074 

x  360)  =.1325 


Mean  specific  heat  =.2400 
and  the  total  heat  value  per  pound  of  gas  above  60  degrees  is 

1209+.  2400  (300  —  60)—  1266  B.  t.  u. 
The  computation  of  the  heat  balance  proper  is  as  follows  : 

Loss  Due  to  Moisture  in  Gas 

The  gas  contains  31  grains  of  moisture  per  cubic  foot.     In 
terms  of  weight  per  pound  of  gas  this  value  is 

(1-^.08164)  x  31  =  379  grains  per  pound 
or  .0541  pounds  of  moisture  per  pound  of  gas. 


In  terms  of  weight  per  pound  of  dry  gas  this  becomes 
.0541-^(1—  .0541)—  .0573  pounds 

The  loss  due  to  the  moisture  content  of  the  gas  per  pound  of 
dry  gas  burned  is  then 

.0573  x  .48  (550  —  60  *)=  13.48  B.  t.  u. 
or 

13.48-7-1266=1.07  per  cent 

Loss  Due  to  Burning  of  Hydrogen 
This  loss  per  pound  of  gas  will  be 

9X  .OO22  [(212  -  60*)  +  970.4+.  48  (550  -  2I2)]  =  26.88  B.  t.  U. 

or 

24.43-7-1266=1.93  per  cent 

Loss  Due  to  Heat  in  Dry  Chimney  Gases 

From  the  flue  gas  analysis  and  formula  (27)  the  weight  of 
dry  gas  per  pound  of  carbon  burned  is 


ii  x  21.2  +  8  x  3.7+7  (74-       . 

—.  —     ,    L  —=12.398  pounds 

3  (2I.2  +  .6) 

The  weight  of  carbon  per  pound  of  dry  gas  burned  is 

From  CO2  .19647  x  ^=.05358 
From  CO    .24473  x  f  =.10488 

Total  €=.15846  pounds 

and  the  weight  of  dry  products  of  combustion  per  pound  of  gas 
burned 

12.398  x  .15846=1.965  pounds 

The  loss  in  dry  chimney  gases  is  then 

1.965  x  .24  (550  —  6o)=23i.o8  B.  t.  u. 
or 

231.08-^-1266=18.25  percent 


*  The  temperature  of  the  atmosphere  is  used  rather  than  the  temperature  of  the  gas 
entering  the  burners,  since  the  heat  balance  is  based  on  the  total  heat  per  pound  of  gas  above 
atmospheric  temperature. 


Loss  Due  to  Incomplete  Combustion  of  Carbon 
This  loss  from  formula  (34)  is 

x  .1585  x  10160—44.30  B.  t.  u. 


21. 
or 

44.30-^-1266—3.50  per  cent 

The  heat  absorbed  by  the  boiler  per  pound  of  gas  burned,  by 
difference,  assuming  the  radiation  and  unaccounted  loss  as  5.0 
per  cent  or  63.30  B.  t.  u.,  is 

1266— (13.48+  24.43  +  231.08+44.30+63. 30)^889.41  B.  t.  u. 
or 

889.41-;- 1 266— 70.25  per  cent 

The  complete  heat  balance  is  then 

B.  t.  u.  Per  Cent 

Loss  due  to  moisture  in  gas     .     .     .     ....       1348  1.07 

Loss  due  to  moisture  formed  in  burning  H2    .       24.43  x-93 

Loss  in  dry  chimney  gases       .     ....     .     231.08  18.25 

Loss  due  to  incomplete  combustion  of  C    ,,     .       44. 30  3.50 

Radiation  and  unaccounted  loss  (assumed)      .       63.30  5.00 

376.59  29.75 

Absorbed  by  boiler  (by  difference)     ....     889.41  70.25 

1266.00  100.00 

The  above  method  may  be  followed  for  any  fuel  where  an 
actual  weight  or  measurement  of  fuel  is  not  possible,  but  where 
such  weight  or  volume  can  be  determined  the  method  used  in 
the  case  of  coal,  preceding,  is  preferable. 


112 


INDEX 


PAGE 

Absolute  temperature 19 

Absolute  zero .19 

Air ii 

and  combustion 42 

Composition  of n 

Effect  of  excess  on  exit  gas  tempera- 
ture    65 

Effect  of  insufficient  on  exit  gas 

temperature 66 

Excess 56,  65,  69 

Insufficient 66,  68 

Loss  due  to  moisture  in  ....  61 
Required  for  combustion  .  ,  .  45,  49 
Supplied  for  combustion  ....  55 
Weight  and  volume  of 16 

Blast  furnace  gas,  computation  of  com- 
bustion data 100 

British  thermal  unit 22 

By-product  coke  oven  gas,  computation 
of  combustion  data 95 


Carbon  dioxide,  specific  heat  of  .     .     . 
Carbon,  loss  due  to  unconsumed     .     . 

Carbon  monoxide,  loss  due  to  pres- 
ence of    . 


3° 
63 

62 


Carbon  monoxide,  specific  heat  of  .     .  31 

Characteristic  equation  of  gases     .    .  15 

Chemistry  of  combustion 9 

Chemical  reactions  of  combustion  .     .  12 

Coal,  computation  of  combustion  data  72 

Combination,  heat  of 20 

Combustion 9 

Air  required  for    .     .     .     .     .     .     45, 49 

Chemical  reactions  of 12 

Chemistry  of 9 

Complete 10, 46 

Computation  of  data,  blast  furnace 

gas 100 

Computation  of  data,by-product  gas  95 

Computation  of  data,  coal     ...  72 

Computation  of  data,  natural  gas  87 


PAGE 

Combustion  ...  9 

Computation  of  data,  oil  ....  83 
Computation  of  data,  wood  ...  78 
General  requirements  of  proper  .  .  70 

Heat  of 20,  22 

Incomplete 62 

Losses 60 

Perfect 46 

Products  of,  weight 45,  50 

Products  of,  volume      .     .     .     .     45,  51 

Speed  of 13 

Temperatures  developed  in   ...      35 

Complete  combustion 10,  46 

Density  of  gases 15,18 

Dissociation 39 

Dulong's  formula 24 

Excess  air 56,  65,  69 

Effect  of  on  exit  gas  temperatures      65 

Flame 39 

Flame  as  a  measure  of  temperature    .      40 

Gas  analysis 47,  58 

Assumptions  of 57 

Conversion  of 19 

Effect  of  presence  of  moisture   .     .      57 

Errors  of 58 

Gases 15 

Characteristic  equation  of     ...       15 

Density  of 15,  18 

Specific  heat  of 32,  34 

Volume  of 15,  18 

Weight  of 15,  18 

Gaseous  fuels,  heat  balance    .     .     .     .     108 

General  conclusions 70 

Heat  balance 60,  105 

Gaseous  fuels 108 

Solid  and  liquid  fuels 105 

Heat  of  combination 20 

Heat  of  combustion       20,  22 

Computation  of 24 

Measurement  of        23 


INDEX —  Continued 


Heat,  specific 28 

Heat  value,  high  and  low 26 

Hydrogen,  loss  due  to  burning   ...  61 

Hydrogen,  specific  heat  of      ....  33 

Ignition,  speed  of 13 

Ignition  temperatures 13 

Incomplete  combustion  of  C,  loss  due  to  62 

Instantaneous  specific  heat     ....  28 

Insufficient  air,  effect  of  on  exit  tem- 
perature         66 

Introduction 7 

Mean  specific  heat 28 

Moisture  in  fuel,  combustion  loss  due  to  60 

Moisture  in  air,  combustion  loss  due  to  61 

Moisture  formed  in  burning  H2,  loss 

due  to 61 

Natural  gas,computation  of  combustion 

data 87 

Nitrogen,  specific  heat  of 31 

Oil,  computation  of  combustion  data  .  83 

Oxygen,  specific  heat  of 33 

Perfect  combustion 46 

Products  of  combustion,  weight      .     45,  50 
Products  of  combustion,  volume      .     45,  51 

Radiation  loss 63 

Reactions,  chemical,  of  combustion     .  12 

Smoke 67 

Solid  and  liquid  fuels,  heat  balance     .  105 

Specific  heat a& 

At  constant  pressure 28 


Specific  heat 28 

At  constant  volume 28 

General  formula 30 

Instantaneous 28 


28 

3° 
31 
33 
3i 

33 


Mean 

OfC02 

Of  CO 

OfH2 

Of  N2 

Of  03      .    ; 

Of  water  vapor 33 

Speed  of  combustion 13 

Sulphur,  effect  on  gas  analysis    ...  53 

Sulphur,  correction  for 54>  57 

Temperature 13 

Absolute 19 

Developed  in  combustion  ....  35 

Effect  of  excess  air  on  exit     ...  65 

Effect  of  insufficient  air  on  exit  .     .  66 

Flame  as  a  measure  of 40 

Ignition 13 

Unaccounted  losses  in  heat  balance    .  63 

Unconsumed  C  in  fuel,  loss  due  to  .     .  63 

Unit,  British  thermal 22 

Volume,  of  air 16 

Volume,  of  gases 18 

Water  vapor,  specific  heat  of  ....  33 

Water  vapor,  in  air,  loss  due  to  ...  61 

Weight  of  air 16 

Weight  of  gases 18 

Wood,  computation  of  combustion  data  78 

Zero,  absolute 19 


114 


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....  -    .. 

I   LIBRARY 

1  6  1947 

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JUN  i  6  1348 

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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


